William D. Banks

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All published works

Action	Title	Year	Authors
+ PDF Chat	A variant of the Linnik-Sprindzuk theorem for simple zeros of Dirichlet L-functions	2024	William D. Banks
+	The Generalized Riemann Hypothesis from zeros of a single <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si6.svg"><mml:mi>L</mml:mi></mml:math>-function	2024	William D. Banks
+ PDF Chat	Shifting the ordinates of zeros of the Riemann zeta function	2024	William D. Banks
+ PDF Chat	Consecutive primes and IP sets	2024	William D. Banks
+	Dense clusters of zeros near the zero-free region of ζ(s)	2024	William D. Banks
+	The Generalized Riemann Hypothesis from zeros of the zeta function	2024	William D. Banks
+ PDF Chat	On the Greatest Common Divisor of Integer Parts of Polynomials	2024	William D. Banks Igor E. Shparlinski
+ PDF Chat	The Riemann Hypothesis via the generalizedvon Mangoldt function	2024	William D. Banks Saloni Sinha
+ PDF	On Ratios of Consecutive Prime Gaps	2023	William D. Banks
+ PDF	Large prime gaps and probabilistic models	2023	William D. Banks Kevin Ford Terence Tao
+ PDF Chat	Towards the Generalized Riemann Hypothesis using only zeros of the Riemann zeta function	2023	William D. Banks
+	Comparing zeros of distinct Dirichlet L-functions	2023	William D. Banks
+	The Generalized Riemann Hypothesis from zeros of the zeta function	2023	William D. Banks
+	Descriptive properties of the type of an irrational number	2023	William D. Banks Asma Harcharras Dominique Lecomte
+	The Generalized Riemann Hypothesis from zeros of a single L-function	2023	William D. Banks
+	The Riemann and Lindelöf hypotheses are determined by thin sets of primes	2022	William D. Banks
+	On the greatest common divisor of integer parts of polynomials	2022	William D. Banks Igor E. Shparlinski
+	Towards the Generalized Riemann Hypothesis using only zeros of the Riemann zeta function	2022	William D. Banks
+	The Riemann Hypothesis via the generalized von Mangoldt Function	2022	William D. Banks Saloni Sinha
+ PDF	On the distribution of reduced fractions with squarefree denominators	2022	William D. Banks
+ PDF Chat	On a conjecture of Soundararajan	2021	William D. Banks Igor E. Shparlinski
+ PDF Chat	Arithmetic progressions of Carmichael numbers in a reduced residue class	2021	William D. Banks
+	Arithmetic progressions of Carmichael numbers in a reduced residue class	2020	William D. Banks
+	On a conjecture of Soundararajan	2020	William D. Banks Igor E. Shparlinski
+	Arithmetic progressions of Carmichael numbers in a reduced residue class	2020	William D. Banks
+ PDF Chat	Congruences with intervals and arbitrary sets	2019	William D. Banks Igor E. Shparlinski
+	Bounds on short character sums and L-functions with characters to a powerful modulus	2019	William D. Banks Igor E. Shparlinski
+ PDF Chat	COUNTING INTEGERS WITH A SMOOTH TOTIENT	2019	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+	Symmetric primes revisited	2019	William D. Banks Paul Pollack Carl Pomerance
+	Congruences with intervals and arbitrary sets	2019	William D. Banks Igor E. Shparlinski
+	Sums with the Möbius function twisted by characters with powerful moduli	2019	William D. Banks Igor E. Shparlinski
+ PDF	On the Dimension of the Jacquet Module of a Certain Induced Representation	2019	William D. Banks Daniel Bump Daniel Lieman
+	Symmetric primes revisited	2019	William D. Banks Paul Pollack Carl Pomerance
+	Large prime gaps and probabilistic models	2019	William D. Banks Kevin Ford Terence Tao
+	Congruences with intervals and arbitrary sets	2019	William D. Banks Igor E. Shparlinski
+ PDF Chat	Consecutive primes and Beatty sequences	2018	William D. Banks Victor Zhenyu Guo
+	Sums with the Mobius function twisted by characters with powerful moduli.	2018	William D. Banks Igor E. Shparlinski
+ PDF	Non-vanishing of Dirichlet series without Euler products	2018	William D. Banks
+	Counting integers with a smooth totient	2018	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+ PDF Chat	On certain zeta functions associated with Beatty sequences	2018	William D. Banks
+	Sums with the Mobius function twisted by characters with powerful moduli	2018	William D. Banks Igor E. Shparlinski
+	On certain zeta functions associated with Beatty sequences	2017	William D. Banks
+	On certain zeta functions associated with Beatty sequences	2017	William D. Banks
+	Consecutive primes and Beatty sequences	2016	William D. Banks Victor Zhenyu Guo
+ PDF	Convolutions with probability distributions, zeros of $L$-functions, and the least quadratic nonresidue	2016	William D. Banks
+	On Coincidences Among Quadratic Fields Generated by the Shanks Sequence	2016	William D. Banks Igor E. Shparlinski
+ PDF Chat	Quadratic nonresidues below the Burgess bound	2016	William D. Banks Victor Z. Guo
+ PDF Chat	Zeta functions and asymptotic additive bases with some unusual sets of primes	2016	William D. Banks
+ PDF Chat	On limit points of the sequence of normalized prime gaps	2016	William D. Banks Tristan Freiberg James Maynard
+	Carmichael numbers and the sieve	2016	William D. Banks Tristan Freiberg
+	On the number of distinct quadratic fields generated by the Shanks sequence	2016	William D. Banks Igor E. Shparlinski
+	Bounds on short character sums and L-functions for characters with a smooth modulus	2016	William D. Banks Igor E. Shparlinski
+	On the number of distinct quadratic fields generated by the Shanks sequence	2016	William D. Banks Igor E. Shparlinski
+	Consecutive primes and Beatty sequences	2016	William D. Banks Victor Zhenyu Guo
+	Quadratic nonresidues below the Burgess bound	2015	William D. Banks Victor Z. Guo
+	Almost primes of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>⌊</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup><mml:mo>⌋</mml:mo></mml:mrow></mml:math>	2015	William D. Banks Victor Z. Guo Igor E. Shparlinski
+ PDF	Fractional parts of Dedekind sums	2015	William D. Banks Igor E. Shparlinski
+	Zeta functions and asymptotic additive bases with some unusual sets of primes	2015	William D. Banks
+	Carmichael numbers and the sieve	2015	William D. Banks Tristan Freiberg
+ PDF	On Gauss sums and the evaluation of Stechkin’s constant	2015	William D. Banks Igor E. Shparlinski
+	CHARACTER SUMS WITH PIATETSKI-SHAPIRO SEQUENCES	2015	Roger C. Baker William D. Banks
+	Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$	2015	William D. Banks Victor Zhenyu Guo Igor E. Shparlinski
+	Every natural number is the sum of forty-nine palindromes	2015	William D. Banks
+ PDF Chat	Consecutive primes in tuples	2015	William D. Banks Tristan Freiberg Caroline L. Turnage‐Butterbaugh
+	Zeta functions and asymptotic additive bases with some unusual sets of primes	2015	William D. Banks
+	Carmichael numbers and the sieve	2015	William D. Banks Tristan Freiberg
+	Quadratic nonresidues below the Burgess bound	2015	William D. Banks Victor Zhenyu Guo
+	Convolutions with probability distributions, zeros of L-functions, and the least quadratic nonresidue	2014	William D. Banks Konstantin A. Makarov
+	Fractional parts of Dedekind sums	2014	William D. Banks Igor E. Shparlinski
+	Sierpiński and Carmichael numbers	2014	William D. Banks Carrie E. Finch Florian Luca Carl Pomerance Pantelimon Stănică
+	OPTIMAL PRIMITIVE SETS WITH RESTRICTED PRIMES	2014	William D. Banks Greg Martin
+ PDF	Waring’s problem for Beatty sequences and a local to global principle	2014	William D. Banks Ahmet M. Güloğlu R. C. Vaughan
+	Fractional parts of Dedekind sums	2014	William D. Banks Igor E. Shparlinski
+	Convolutions with probability distributions, zeros of L-functions, and the least quadratic nonresidue	2014	William D. Banks Konstantin A. Makarov
+	Consecutive primes in tuples	2013	William D. Banks Tristan Freiberg Caroline L. Turnage‐Butterbaugh
+	On Gauss sums and the evaluation of Stechkin's constant	2013	William D. Banks Igor E. Shparlinski
+	Piatetski-Shapiro primes from almost primes	2013	Roger C. Baker William D. Banks Zhenyu V. Guo Aaron Yeager
+ PDF Chat	Self-intersections of the Riemann zeta function on the critical line	2013	William D. Banks Victor Castillo-Garate Luigi Fontana Carlo Morpurgo
+	Optimal primitive sets with restricted primes	2013	William D. Banks Greg Martin
+	Optimal primitive sets with restricted primes	2013	William D. Banks Greg Martin
+	Consecutive primes in tuples	2013	William D. Banks Tristan Freiberg Caroline L. Turnage‐Butterbaugh
+	On Gauss sums and the evaluation of Stechkin's constant	2013	William D. Banks Igor E. Shparlinski
+	Optimal primitive sets with restricted primes	2013	William D. Banks Greg S. Martin
+ PDF Chat	Piatetski-Shapiro sequences	2012	Roger C. Baker William D. Banks Jörg Brüdern Igor E. Shparlinski Andreas Weingartner
+	Self-intersections of the Riemann zeta function on the critical line	2012	William D. Banks Victor Castillo-Garate Luigi Fontana Carlo Morpurgo
+ PDF	Carmichael Meets Chebotarev	2012	William D. Banks Ahmet M. Güloğlu Aaron Yeager
+ PDF	On Repeated Values of the Riemann Zeta Function on the Critical Line	2012	William D. Banks Sarah Kang
+	Piatetski-Shapiro sequences	2012	Roger C. Baker William D. Banks Jörg Brüdern Igor E. Shparlinski Andreas Weingartner
+ PDF	On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields	2012	William D. Banks Francesco Pappalardi Igor E. Shparlinski
+ PDF	EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS	2012	William D. Banks John Friedlander Moubariz Z. Garaev Igor E. Shparlinski
+	Self-intersections of the Riemann zeta function on the critical line	2012	William D. Banks Victor Castillo-Garate Luigi Fontana Carlo Morpurgo
+	Piatetski-Shapiro sequences	2012	Roger C. Baker William D. Banks Jörg Brüdern Igor E. Shparlinski Andreas Weingartner
+	Carmichael numbers with a totient of the form a 2 + nb 2	2011	William D. Banks
+ PDF Chat	Sums and products with smooth numbers	2011	William D. Banks David Covert
+	Power Totients with Almost Primes	2011	William D. Banks Florian Luca
+ PDF	Carmichael numbers composed of primes from a Beatty sequence	2011	William D. Banks Aaron Yeager
+	Sums and Products with Smooth Numbers	2010	William D. Banks David Covert
+	Sums with convolutions of Dirichlet characters	2010	William D. Banks Igor E. Shparlinski
+ PDF	ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS	2010	William D. Banks Carl Pomerance
+	On group structures realized by elliptic curves over arbitrary finite fields	2010	William D. Banks Francesco Pappalardi Igor E. Shparlinski
+ PDF Chat	On primitive Dirichlet characters and the Riemann hypothesis	2010	William D. Banks Ahmet M. Güloğlu C. Wesley Nevans
+	Sums and Products with Smooth Numbers	2010	William D. Banks David S. Covert
+	On group structures realized by elliptic curves over arbitrary finite fields	2010	William D. Banks Francesco Pappalardi Igor E. Shparlinski
+ PDF Chat	Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height	2009	William D. Banks Igor E. Shparlinski
+ PDF	A REMARK ON GIUGA’S CONJECTURE AND LEHMER’S TOTIENT PROBLEM	2009	William D. Banks C. Wesley Nevans Carl Pomerance
+ PDF	Uniform Distribution of Fractional Parts Related to Pseudoprimes	2009	William D. Banks Moubariz Z. Garaev Florian Luca Igor E. Shparlinski
+ PDF	Carmichael Numbers with a Square Totient	2009	William D. Banks
+ PDF	Prime numbers with Beatty sequences	2009	William D. Banks Igor E. Shparlinski
+ PDF	Values of the Carmichael Function Equal to a Sum of Two Squares	2009	William D. Banks Ahmet M. Güloğlu
+ PDF	Arithmetic functions on Beatty sequences	2008	Alex G. Abercrombie William D. Banks Igor E. Shparlinski
+ PDF	A VARIANT ON THE NOTION OF A DIOPHANTINE <i>s</i>-TUPLE	2008	William D. Banks Florian Luca László Szalay
+	CONGRUENCES AND EXPONENTIAL SUMS WITH THE SUM OF ALIQUOT DIVISORS FUNCTION	2008	Sanka Balasuriya William D. Banks Igor E. Shparlinski
+ PDF	The Nicolas and Robin inequalities with sums of two squares	2008	William D. Banks Derrick Hart Pieter Moree C. Wesley Nevans
+	MULTIPLICATIVE CHARACTER SUMS WITH TWICE-DIFFERENTIABLE FUNCTIONS	2008	William D. Banks Igor E. Shparlinski
+ PDF Chat	Density of non-residues in Burgess-type intervals and applications	2008	William D. Banks M. Z. Garaev D. R. Heath‐Brown Igor E. Shparlinski
+ PDF Chat	Integers without divisors from a fixed arithmetic progression	2008	William D. Banks John Friedlander Florian Luca
+	On primitive Dirichlet characters and the Riemann hypothesis	2008	William D. Banks Ahmet M. Güloğlu C. Wesley Nevans
+	The Nicolas and Robin inequalities with sums of two squares	2007	William D. Banks Derrick Hart Pieter Moree C. Wesley Nevans
+ PDF	WHEN THE SUM OF ALIQUOTS DIVIDES THE TOTIENT	2007	William D. Banks Florian Luca
+	Estimates for Wieferich numbers	2007	William D. Banks Florian Luca Igor E. Shparlinski
+ PDF	Integers with a Large Smooth Divisor	2007	William D. Banks Igor E. Shparlinski
+ PDF	On Rough and Smooth Neighbors	2007	William D. Banks Igor E. Shparlinski Florian Luca
+ PDF	On values taken by the largest prime factor of shifted primes	2007	William D. Banks Igor E. Shparlinski
+ PDF	Representations of integers as sums of primes from a Beatty sequence	2007	William D. Banks Ahmet M. Güloğlu C. Wesley Nevans
+	Prime numbers with Beatty sequences	2007	William D. Banks Igor E. Shparlinski
+	Exponential sums with polynomial values of the discrete logarithm	2007	William D. Banks Igor E. Shparlinski
+	The Nicolas and Robin inequalities with sums of two squares	2007	William D. Banks Derrick Hart Pieter Moree C. Wesley Nevans
+	Sums of prime divisors and Mersenne numbers	2007	William D. Banks Florian Luca
+ PDF	Congruences and Rational Exponential Sums with the Euler Function	2006	William D. Banks Igor E. Shparlinski
+	Prime divisors in Beatty sequences	2006	William D. Banks Igor E. Shparlinski
+	Density of non-residues in short intervals	2006	William D. Banks M. Z. Garaev D. R. Heath‐Brown Igor E. Shparlinski
+ PDF	Non-residues and primitive roots in Beatty sequences	2006	William D. Banks Igor E. Shparlinski
+	Character sums with exponential functions over smooth numbers	2006	William D. Banks John Friedlander Moubariz Z. Garaev Igor E. Shparlinski
+	Composite Integers n for Which ϕ(n)\|n – 1	2006	William D. Banks Florian Luca
+	Multiplicative character sums with the sum of g-ary Digits Function	2006	William D. Banks Igor E. Shparlinski
+ PDF	Arithmetic properties of $φ(n)/λ(n)$ and the structure of the multiplicative group modulo $n$	2006	William D. Banks Florian Luca Igor E. Shparlinski
+	Values of the Euler function free of kth powers	2006	William D. Banks Francesco Pappalardi
+ PDF	Incomplete exponential sums and Diffie–Hellman triples	2006	William D. Banks John Friedlander Sergeĭ Konyagin Igor E. Shparlinski
+ PDF	Average Value of the Euler Function on Binary Palindromes	2006	William D. Banks Igor E. Shparlinski
+ PDF	Short character sums with Beatty sequences	2006	William D. Banks Igor E. Shparlinski
+ PDF	Coincidences in the values of the Euler and Carmichael functions	2006	William D. Banks John Friedlander Florian Luca Francesco Pappalardi Igor E. Shparlinski
+	Integers with a large smooth divisor	2006	William D. Banks Igor E. Shparlinski
+	Character sums with Beatty sequences on Burgess-type intervals	2006	William D. Banks Igor E. Shparlinski
+	On integers with a special divisibility property	2006	William D. Banks Florian Luca
+	Squares from products of integers	2006	William D. Banks A. J. van der Poorten
+	Integers without divisors from a fixed arithmetic progression	2006	William D. Banks John Friedlander Florian Luca
+	Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height	2006	William D. Banks Igor E. Shparlinski
+ PDF	Compositions with the euler and carmichael functions	2005	William D. Banks Florian Luca Filip Saidak P. StĂ nicĂ
+ PDF	Distributional properties of the largest prime factor	2005	William D. Banks Glyn Harman Igor E. Shparlinski
+ PDF	SOME DIVISIBILITY PROPERTIES OF THE EULER FUNCTION	2005	William D. Banks Florian Luca Igor E. Shparlinski
+ PDF	Prime divisors of palindromes	2005	William D. Banks Igor E. Shparlinski
+ PDF	Irrationality of Power Series for Various Number Theoretic Functions	2005	William D. Banks Florian Luca Igor E. Shparlinski
+ PDF	Values of arithmetical functions equal to a sum of two squares	2005	William D. Banks Florian Luca Filip Saidak§ Igor E. Shparlinski
+ PDF	Values of the Euler Function in Various Sequences	2005	William D. Banks Kevin Ford Florian Luca Francesco Pappalardi Igor E. Shparlinski
+	On the Value Set of n! Modulo a Prime	2005	William D. Banks
+	Uniform distribution of the fractional part of the average prime divisor	2005	William D. Banks Moubariz Z. Garaev Florian Luca Igor E. Shparlinski
+	Concatenations with Binary Recurrent Sequences	2005	William D. Banks Florian Luca
+	None	2005	William D. Banks D. R. Heath‐Brown Igor E. Shparlinski
+ PDF	Roughly squarefree values of the Euler and Carmichael functions	2005	William D. Banks Florian Luca
+ PDF	Nonaliquots and Robbins numbers	2005	William D. Banks Florian Luca
+	Uniform Distribution of Fractional Parts Related to Pseudoprimes	2005	William D. Banks Moubariz Z. Garaev Florian Luca Igor E. Shparlinski
+ PDF	Smooth values of shifted primes in arithmetic progressions	2004	William D. Banks Asma Harcharras Igor E. Shparlinski
+ PDF	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+ PDF	Congruences and exponential sums with the Euler function	2004	William D. Banks Igor E. Shparlinski
+	Noncototients and Nonaliquots	2004	William D. Banks Florian Luca
+ PDF	Almost All Palindromes Are Composite	2004	William D. Banks Derrick Hart Mayumi Sakata
+ PDF	Number Theoretic Designs for Directed Regular Graphs of Small Diameter	2004	William D. Banks Alessandro Conflitti Igor E. Shparlinski
+ PDF	Arithmetic properties of numbers with restricted digits	2004	William D. Banks Igor E. Shparlinski
+	Almost all palindromes are composite	2004	William D. Banks Derrick Hart Mayumi Sakata
+ PDF	Exponential sums over Mersenne numbers	2003	William D. Banks Alessandro Conflitti John Friedlander Igor E. Shparlinski
+ PDF	New examples of noncommutative $Łambda(p)$ sets	2003	William D. Banks Asma Harcharras
+ PDF	Short Kloosterman Sums for Polynomials over Finite Fields	2003	William D. Banks Asma Harcharras Igor E. Shparlinski
+	Matrix inequalities with applications to the theory of iterated kernels	2003	William D. Banks Asma Harcharras Stefan Neuwirth Éric Ricard
+ PDF	None	2003	William D. Banks Daniel Bump Daniel Lieman
+	New examples of noncommutative Λ(p) sets	2003	William D. Banks Asma Harcharras
+ PDF	Average normalisations of elliptic curves	2002	William D. Banks Igor E. Shparlinski
+	On the Number of Sparse RSA Exponents	2002	William D. Banks Igor E. Shparlinski
+	On the Number of Sparse RSA Exponents	2002	William D. Banks
+ PDF	Character sums over integers with restricted $g$-ary digits	2002	William D. Banks Alessandro Conflitti Igor E. Shparlinski
+	None	2001	William D. Banks
+	Block-compatible metaplectic cocycles	1999	William D. Banks Jason Levy Mark R. Sepanski
+ PDF	Heredity of Whittaker models on the metaplectic group	1998	William D. Banks
+ PDF	A Corollary to Bernstein’s Theorem and Whittaker Functionals on the Metaplectic Group	1998	William D. Banks
+	Twisted symmetric-square L-functions and the nonexistence of Siegel zeros on GL(3)	1997	William D. Banks
+ PDF	The Casselman-Shalika Formula for a Distinguished Model	1995	William D. Banks
+ PDF	The Casselman-Shalika formula for a distinguished model	1995	William D. Banks

Common Coauthors

Coauthor	Papers Together
Igor E. Shparlinski	79
Florian Luca	25
John Friedlander	10
Carl Pomerance	8
Tristan Freiberg	7
C. Wesley Nevans	7
Francesco Pappalardi	6
Ahmet M. Güloğlu	6
Asma Harcharras	5
Victor Zhenyu Guo	5
Moubariz Z. Garaev	5
Derrick Hart	5
Roger C. Baker	5
Alessandro Conflitti	3
Pieter Moree	3
Kevin Ford	3
Carlo Morpurgo	3
Caroline L. Turnage‐Butterbaugh	3
Victor Castillo-Garate	3
Aaron Yeager	3
Jörg Brüdern	3
Andreas Weingartner	3
Victor Z. Guo	3
D. R. Heath‐Brown	3
Greg Martin	3
Luigi Fontana	3
Daniel Bump	2
Daniel Lieman	2
Mayumi Sakata	2
Paul Pollack	2
Konstantin A. Makarov	2
M. Z. Garaev	2
Saloni Sinha	2
David Covert	2
Terence Tao	2
R. C. Vaughan	1
Jason Levy	1
Sergeĭ Konyagin	1
A. J. van der Poorten	1
Stefan Neuwirth	1
Filip Saidak§	1
Pantelimon Sta ̆ Nica	1
Glyn Harman	1
Carrie E. Finch	1
Sanka Balasuriya	1
Zhenyu V. Guo	1
Asma Harcharras	1
Greg S. Martin	1
Éric Ricard	1
Sarah Kang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	29
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	20
+ PDF	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum	19
+	Multiplicative Number Theory	1980	H. Davenport	19
+	There are Infinitely Many Carmichael Numbers	1994	W. R. Alford Andrew Granville Carl Pomerance	18
+ PDF	Shifted primes without large prime factors	1998	Roger C. Baker G. Harman	17
+	Uniform distribution of sequences	1974	L. Kuipers Harald Niederreiter	17
+	On a problem of Oppenheim concerning “factorisatio numerorum”	1983	E. Rodney Canfield Paul Erdös Carl Pomerance	14
+	Analytic Number Theory	2004	Emmanuel Kowalski Henryk Iwaniec	13
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan	12
+	On The Number of Positive Integers ≤ x and Free of Prime Factors > y	1951	N.G. de Bruijn	11
+	On the Normal Behavior of the Iterates Of some Arithmetic Functions	1990	Paul Erdös Andew Granvilie Carl Pomerance Claudia Spiro	11
+	Zur metrischen Theorie der diophantischen Approximationen	1926	A. Khintchine	11
+	Rational approximations to algebraic numbers	1955	H. Davenport K. F. Roth	11
+ PDF	The large sieve	1973	Hugh L. Montgomery R. C. Vaughan	10
+ PDF	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski	10
+	The Method of Trigonometrical Sums in the Theory of Numbers	2004	Ivan Matveevich Vinogradov K. F. Roth Anne Ashley Davenport	10
+	Character Sums with Exponential Functions and their Applications	1999	Sergeĭ Konyagin Igor E. Shparlinski	9
+	Das asymptotische Verhalten von Summen �ber multiplikative Funktionen	1961	Eduard Wirsing	9
+ PDF	Non-residues and primitive roots in Beatty sequences	2006	William D. Banks Igor E. Shparlinski	9
+	ON THE DISTRIBUTION OF DIGITS IN PERIODIC FRACTIONS	1972	N. M. Korobov	9
+	On the number of positive integers ≦ x and free of prime factors > y	1986	Adolf Hildebrand	9
+ PDF	Short character sums with Beatty sequences	2006	William D. Banks Igor E. Shparlinski	9
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	9
+ PDF	Beatty sequences and multiplicative number theory	1995	Alex G. Abercrombie	9
+	A Generating Function Technique for Beatty Sequences and Other Step Sequences	2002	Kevin O’Bryant	8
+ PDF	An introduction to the theory of numbers	1960	G. H. Hardy	8
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown	7
+	On an analogue of the Dirichlet divisor problem	2004	A.V. Begunts	7
+ PDF	On the normal number of prime factors of $\phi(n)$	1985	Paul Erdös Carl Pomerance	7
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős	7
+	On zeros of Dirichlet'sL series	1974	Henryk Iwaniec	7
+ PDF	ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS	2010	William D. Banks Carl Pomerance	7
+ PDF	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld	7
+	The distribution of quadratic residues and non‐residues	1957	D. A. Burgess	7
+	Approximation by algebraic numbers	2006	Yann Bugeaud	7
+ PDF	Primes in arithmetic progressions	1996	Olivier Ramaré Robert Rumely	7
+	Primes in progressions to prime-power modulus	1972	P. X. Gallagher	6
+	Exponential Sums and their Applications	1992	N. M. Korobov	6
+	On the Arithmetic Structure of Sets Characterized by Sum of Digits Properties	1996	Christian Mauduit Andràs Sárközy	6
+ PDF	New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum	2000	D. R. Heath‐Brown	6
+ PDF Chat	Density of non-residues in Burgess-type intervals and applications	2008	William D. Banks M. Z. Garaev D. R. Heath‐Brown Igor E. Shparlinski	6
+	The square-free divisor problem II	1996	Roger C. Baker	6
+	The Riemann Zeta-Function	1992	A. A. Karatsuba Сергей Воронин	6
+ PDF Chat	Short character sums for composite moduli	2014	Mei-Chu Chang	6
+	Van der Corput's Method of Exponential Sums	1991	S. W. Graham Grigori Kolesnik	6
+ PDF	On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ	2002	Florian Luca Carl Pomerance	6
+ PDF	A note on the least quadratic non-residue of the integer-sequences	2003	M. Z. Garaev	6
+	On the Distribution of Diffie--Hellman Triples with Sparse Exponents	2001	John Friedlander Igor E. Shparlinski	6
+	Sieves in Number Theory	2001	G. N. Greaves	6