Kevin Broughan

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All published works

Action	Title	Year	Authors
+	Propositional Calculus P0	2023	Kevin Broughan
+	Equivalents of the Riemann Hypothesis	2023	Kevin Broughan
+	The Decidability of the Riemann Hypothesis	2023	Kevin Broughan
+	Bounded Gaps Between Primes	2021	Kevin Broughan
+	The Dispersion Method of Linnik	2021	Kevin Broughan
+	Bessel Functions of the First Kind	2021	Kevin Broughan
+	Maynard’s Radical Simplification	2021	Kevin Broughan
+	Further Work and the Epilogue	2021	Kevin Broughan
+	The Weil Exponential Sum Bound	2021	Kevin Broughan
+	Variations on Bombieri–Vinogradov	2021	Kevin Broughan
+	Complex Function Theory	2021	Kevin Broughan
+	The Sieves of Brun and Selberg	2021	Kevin Broughan
+	Polymath’s Refinements of Maynards Results	2021	Kevin Broughan
+	Solving an Optimization Problem	2021	Kevin Broughan
+	A Type of Compact Symmetric Operator	2021	Kevin Broughan
+	The Breakthrough of Goldston, Motohashi, Pintz and Yildirim	2021	Kevin Broughan
+	A Brun–Titchmarsh Inequality	2021	Kevin Broughan
+	Early Work	2021	Kevin Broughan
+	Introduction	2021	Kevin Broughan
+	The Astounding Result of Yitang Zhang	2021	Kevin Broughan
+	Numbers That Do Not Satisfy Robin's Inequality	2017	Kevin Broughan
+	The Riemann Zeta Function	2017	Kevin Broughan
+	Other Equivalents to the Riemann Hypothesis	2017	Kevin Broughan
+	Euler's Totient Function	2017	Kevin Broughan
+	Robin's Theorem	2017	Kevin Broughan
+	Banach and Hilbert Spaces	2017	Kevin Broughan
+	Banach and Hilbert Space Methods	2017	Kevin Broughan
+	Dirichlet <i>L</i>-Functions	2017	Kevin Broughan
+	The Riemann Xi Function	2017	Kevin Broughan
+	Weil's Explicit Formula, Inequality and Conjectures	2017	Kevin Broughan
+	Equivalents of the Riemann Hypothesis	2017	Kevin Broughan
+	Cyclotomic Polynomials	2017	Kevin Broughan
+	The Riemann–Stieltjes Integral	2017	Kevin Broughan
+	Equivalents of the Riemann Hypothesis	2017	Kevin Broughan
+	The Riemann Zeta Function	2017	Kevin Broughan
+	Convergence of Series	2017	Kevin Broughan
+	Orthogonal Polynomials	2017	Kevin Broughan
+	Corrigendum: A conjecture of De Koninck regarding particular values of the sum of divisors function	2017	Kevin Broughan Daniel Delbourgo
+	Robin's inequality for 11-free integers	2015	Kevin Broughan Timothy S. Trudgian
+	Quadrafree factorisatio numerorum	2014	Kevin Broughan
+	On the Ratio of the Sum of Divisors and Euler's Totient Function II	2014	Kevin Broughan Qizhi Zhou
+	A conjecture of De Koninck regarding particular square values of the sum of divisors function	2013	Kevin Broughan Daniel Delbourgo Qizhi Zhou
+ PDF Chat	Perfect repdigits	2013	Kevin Broughan Sergio Guzmán Sanchez Florian Luca
+ PDF Chat	On square values of the product of the Euler totient and sum of divisors functions	2013	Kevin Broughan Kevin Ford Florian Luca
+ PDF Chat	ON SHIFTED PRIMES AND BALANCED PRIMES	2012	Kevin Broughan
+	Sum-Products Estimates with Several Sets and Applications	2012	Antal Balog Kevin Broughan Igor E. Shparlinski
+	An Explicit Bound for Aliquot Cycles of Repdigits	2012	Kevin Broughan
+	On Integers for Which the Sum of Divisors is the Square of the Squarefree Core	2012	Kevin Broughan Jean-Marie De Koninck Imre K ́atai Florian Luca
+	Odd Repdigits to Small Bases Are Not Perfect	2012	Kevin Broughan Qizhi Zhou
+ PDF Chat	Gram lines and the average of the real part of the Riemann zeta function	2011	Kevin Broughan A.R. Barnett
+ PDF Chat	There are No Multiply-Perfect Fibonacci Numbers	2011	Kevin Broughan Marcos J. González Ryan H. Lewis Florian Luca V. Janitzio Mejía Huguet Alain Togbé
+ PDF Chat	On the number of solutions of exponential congruences	2011	Antal Balog Kevin Broughan Igor E. Shparlinski
+	On the Number of Solutions of Exponential Congruences	2010	Antal Balog Kevin Broughan Igor E. Shparlinski
+ PDF Chat	On the Fürstenberg closure of a class of binary recurrences	2010	Kevin Broughan Florian Luca
+	Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4	2010	Kevin Broughan Qizhi Zhou
+	Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem	2010	Kevin Broughan Florian Luca Igor E. Shparlinski
+	On the Number of Solutions of Exponential Congruences	2010	Antal Balog Kevin Broughan Igor E. Shparlinski
+	Appendix: The GL(n)pack Manual	2009	Kevin Broughan Dorian Goldfeld
+ PDF Chat	FLAT PRIMES AND THIN PRIMES	2009	Kevin Broughan Qizhi Zhou
+ PDF Chat	An algorithm for the explicit evaluation of GL( <i>n</i> ;R) Kloosterman sums	2009	Kevin Broughan
+ PDF Chat	Extension of the Riemann ξ-Function's Logarithmic Derivative Positivity Region to Near the Critical Strip	2009	Kevin Broughan
+ PDF Chat	QUALIFIED DIFFERENCE SETS FROM UNIONS OF CYCLOTOMIC CLASSES	2009	Kevin Byard Kevin Broughan
+	On the subsequence of primes having prime subscripts	2009	Kevin Broughan A.R. Barnett
+ PDF Chat	Evaluating Jacquet’s $\mathbf {{\rm GL}(n)}$ Whittaker function	2008	Kevin Broughan
+ PDF Chat	Corrigendum to ``The holomorphic flow of the Riemann zeta function''	2007	Kevin Broughan A.R. Barnett
+	Odd multiperfect numbers of abundancy 4	2007	Kevin Broughan Qizhi Zhou
+ PDF Chat	Corrigenda for Holomorphic Flows on Simply Connected Regions have No Limit Cycles	2007	Kevin Broughan
+	The Average Order of the Dirichlet Series of the gcd-sum Function	2007	Kevin Broughan
+	Linear law for the logarithms of the Riemann periods at simple critical zeta zeros	2005	Kevin Broughan A.R. Barnett
+ PDF Chat	The holomorphic flow of Riemann's function ξ(<i>z</i>)	2005	Kevin Broughan
+ PDF Chat	Harmonic sets and the harmonic prime number theorem	2005	Kevin Broughan Rory J. Casey
+	A note on Casimir operators for the generalized upper half plane	2005	Kevin Broughan
+	Characterizing the sum of two cubes.	2003	Kevin Broughan
+ PDF Chat	The holomorphic flow of the Riemann zeta function	2003	Kevin Broughan A.R. Barnett
+ PDF Chat	Adic Topologies for the Rational Integers	2003	Kevin Broughan
+	Characterizing the Sum of Two Cubes Version: 18th December 2003.	2003	Kevin Broughan
+ PDF Chat	None	2003	Kevin Broughan
+ PDF Chat	Asymptotic Order of the Square-free Part of N!	2002	Kevin Broughan
+ PDF Chat	Vanishing of the integral of the Hurwitz zeta Function	2002	Kevin Broughan
+	Asymptotic order of the square free part of n	2002	Kevin Broughan
+ PDF Chat	Restricted divisor sums	2002	Kevin Broughan
+	Relaxations of the ABC conjecture using integer k'th roots	2002	Kevin Broughan
+	The gcd-sum function	2001	Kevin Broughan
+	GEOMETRY AND ORDER OF CHAOS	1999	Jan Awrejcewicz Claude‐Henri Lamarque Kevin Broughan
+	Some symbolic computing links to the NAG numeric library	1991	Kevin Broughan Grant Keady T. D. Robb M. G. Richardson Michael C. Dewar
+ PDF Chat	Topologies induced by metrics with disconnected range	1982	Kevin Broughan
+	Four Metric Conditions Characterizing Cech Dimension Zero	1977	Kevin Broughan
+ PDF Chat	The boundedness principle characterizes second category subsets	1977	Kevin Broughan
+ PDF Chat	The intersection of a continuum of open dense sets	1977	Kevin Broughan
+ PDF Chat	Four metric conditions characterizing Čech dimension zero	1977	Kevin Broughan
+	Uniform spaces	1975	Kevin Broughan
+ PDF Chat	On the Number of Structures of Reflexive and Transitive Relations	1973	Kevin Broughan
+ PDF Chat	Metrization of spaces having Čech dimension zero	1973	Kevin Broughan
+	Uniformization of topological spaces with small inductive dimension zero	1973	Kevin Broughan
+ PDF Chat	A metric characterizing Čech dimension zero	1973	Kevin Broughan

Common Coauthors

Coauthor	Papers Together
Qizhi Zhou	6
Florian Luca	6
A.R. Barnett	5
Igor E. Shparlinski	5
Antal Balog	4
Daniel Delbourgo	2
Michael C. Dewar	1
Timothy S. Trudgian	1
Ryan H. Lewis	1
Jan Awrejcewicz	1
Marcos J. González	1
T. D. Robb	1
Imre K ́atai	1
V. Janitzio Mejía Huguet	1
Sergio Guzmán Sanchez	1
Jean-Marie De Koninck	1
Alain Togbé	1
Claude‐Henri Lamarque	1
Dorian Goldfeld	1
Grant Keady	1
M. G. Richardson	1
Kevin Ford	1
Rory J. Casey	1
Kevin Byard	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol	13
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld	9
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown	6
+	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.	6
+	Riemann's Zeta Function	1974	Harold M. Edwards	6
+ PDF Chat	None	2003	Kevin Broughan	6
+ PDF Chat	Existence of primitive divisors of Lucas and Lehmer numbers	2001	Yonatan Bilu Guillaume Hanrot Paul Voutier	4
+ PDF Chat	On the zeros of the Riemann zeta function in the critical strip	1979	Richard P. Brent	4
+	Automorphic Forms and L-Functions for the Group Gl(n, R)	2006	Dorian Goldfeld	4
+	On Integers for Which the Sum of Divisors is the Square of the Squarefree Core	2012	Kevin Broughan Jean-Marie De Koninck Imre K ́atai Florian Luca	4
+	Introduction to Analytic Number Theory	1976	Tom M. Apostol	4
+ PDF Chat	The holomorphic flow of the Riemann zeta function	2003	Kevin Broughan A.R. Barnett	4
+ PDF Chat	Unsolved Problems in Number Theory	1994	Richard K. Guy	4
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	4
+	Modular Functions and Dirichlet Series in Number Theory	1990	Tom M. Apostol	4
+ PDF Chat	Additive number theory: the classical bases	1997	S Axier E Gehring Paul R. Halmos Melvyn B. Nathanson S Axler F. W. Gehring	4
+ PDF Chat	On the Zeros of the Riemann Zeta Function in the Critical Strip. IV	1986	J. Lune H. J. J. te Riele D.T. Winter	3
+	Perfect fibonacci and lucas numbers	2000	Florian Luca	3
+ PDF Chat	The large sieve	1973	Hugh L. Montgomery R. C. Vaughan	3
+	Multiplicative Number Theory	1980	H. Davenport	3
+	On the Numerical Factors of the Arithmetic Forms α n ± β n	1913	R. D. Carmichael	3
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	3
+ PDF Chat	Metrization of spaces having Čech dimension zero	1973	Kevin Broughan	3
+	On a problem of Oppenheim concerning “factorisatio numerorum”	1983	E. Rodney Canfield Paul Erdős Carl Pomerance	3
+	Basic Analytic Number Theory	1993	Anatolij A. Karatsuba Melvyn B. Nathanson	3
+	Multiperfect numbers with identical digits	2010	Florian Luca Paul Pollack	3
+	Elementary Methods in Number Theory	2000	Melvyn B. Nathanson	3
+ PDF Chat	Old and new conjectured diophantine inequalities	1990	Serge Lang	3
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős	3
+	An Introduction to the Theory of the Riemann Zeta-Function	1988	S. J. Patterson	3
+ PDF Chat	Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes	1923	G. H. Hardy J. E. Littlewood	3
+	On the large sieve	1965	Enrico Bombieri	3
+ PDF Chat	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski	2
+ PDF Chat	The sum-product estimate for large subsets of prime fields	2008	M. Z. Garaev	2
+ PDF Chat	A heuristic asymptotic formula concerning the distribution of prime numbers	1962	Paul T. Bateman Roger A. Horn	2
+ PDF Chat	On the distribution of spacings between zeros of the zeta function	1987	Andrew Odlyzko	2
+	On divisors of binomial coefficients, I	1985	Andràs Sárközy	2
+	History of the Theory of Numbers	1919	L. E. Dickson	2
+ PDF Chat	On the class number of imaginary quadratic fields	1971	A. Baker	2
+ PDF Chat	Some heuristics and results for small cycles of the discrete logarithm	2005	Joshua Holden Pieter Moree	2
+ PDF Chat	On some inequalities for the gamma and psi functions	1997	Horst Alzer	2
+	Asymptotics and Special Functions	1997	F. W. J. Olver	2
+	Kloosterman sums and Fourier coefficients of cusp forms	1982	Jean-Marc Deshouillérs Henryk Iwaniec	2
+	ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES	1973	Chen Jing-Run	2
+ PDF Chat	Zeros of the derivatives of the Riemann zeta-function	1974	Norman Levinson Hugh L. Montgomery	2
+ PDF Chat	On the equation of Catalan	1976	R. Tijdeman	2
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	2
+ PDF Chat	A metric characterizing Čech dimension zero	1973	Kevin Broughan	2
+	The Riemann Zeros and Eigenvalue Asymptotics	1999	Michael Berry Jonathan P. Keating	2
+	Geometrisches zur Riemannschen Zetafunktion	1935	Andreas Speiser	2