Adam J. Harper

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All published works

Action	Title	Year	Authors
+ PDF Chat	Simple Barban--Davenport--Halberstam type asymptotics for general sequences	2024	Adam J. Harper
+ PDF Chat	Moments of random multiplicative functions, III: A short review	2024	Adam J. Harper
+	The typical size of character and zeta sums is $o(\sqrt{x})$	2023	Adam J. Harper
+	A note on character sums over short moving intervals	2022	Adam J. Harper
+	Almost Sure Large Fluctuations of Random Multiplicative Functions	2021	Adam J. Harper
+ PDF Chat	MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS	2020	Adam J. Harper
+	Exposé Bourbaki 1161 : The Riemann zeta function in short intervals after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan	2020	Adam J. Harper
+	Almost sure large fluctuations of random multiplicative functions	2020	Adam J. Harper
+ PDF Chat	Moments of random multiplicative functions, II: High moments	2019	Adam J. Harper
+ PDF Chat	Extreme biases in prime number races with many contestants	2019	Kevin Ford Adam J. Harper Youness Lamzouri
+	The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]	2019	Adam J. Harper
+	On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture	2019	Adam J. Harper
+ PDF Chat	A new proof of Halász’s theorem, and its consequences	2018	Andrew Granville Adam J. Harper K. Soundararajan
+	A more intuitive proof of a sharp version of Halász’s theorem	2018	Andrew Granville Adam J. Harper K. Soundararajan
+	Extreme biases in prime number races with many contestants	2017	Kevin Ford Adam J. Harper Youness Lamzouri
+	Orderings of weakly correlated random variables, and prime number races with many contestants	2017	Adam J. Harper Youness Lamzouri
+	Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos	2017	Adam J. Harper
+ PDF Chat	Maxima of a randomized Riemann zeta function, and branching random walks	2017	Louis‐Pierre Arguin David Belius Adam J. Harper
+	A more intuitive proof of a sharp version of Halász's theorem	2017	Andrew Granville Adam J. Harper K. Soundararajan
+	Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos	2017	Adam J. Harper
+	Extreme biases in prime number races with many contestants	2017	Kevin R. Ford Adam J. Harper Youness Lamzouri
+	Pickands’ constant $H_{\alpha}$ does not equal $1/\Gamma(1/\alpha)$, for small $\alpha$	2016	Adam J. Harper
+ PDF Chat	LOWER BOUNDS FOR THE VARIANCE OF SEQUENCES IN ARITHMETIC PROGRESSIONS: PRIMES AND DIVISOR FUNCTIONS	2016	Adam J. Harper K. Soundararajan
+ PDF Chat	Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers	2016	Adam J. Harper
+	Lower bounds for the variance of sequences in arithmetic progressions: primes and divisor functions	2016	Adam J. Harper K. Soundararajan
+	Lower bounds for the variance of sequences in arithmetic progressions: primes and divisor functions	2016	Adam J. Harper K. Soundararajan
+ PDF Chat	Mean values of multiplicative functions over function fields	2015	Andrew Granville Adam J. Harper K. Soundararajan
+	Orderings of weakly correlated random variables, and prime number races with many contestants	2015	Adam J. Harper Youness Lamzouri
+	Maxima of a randomized Riemann zeta function, and branching random walks	2015	Louis‐Pierre Arguin David Belius Adam J. Harper
+	A note on Helson's conjecture on moments of random multiplicative functions	2015	Adam J. Harper Ashkan Nikeghbali Maksym Radziwiłł
+	Mean values of multiplicative functions over function fields	2015	Andrew Granville Adam J. Harper K. Soundararajan
+	EXAMPLE SHEET 1 FOR CAMBRIDGE PART III COURSE ON “ELEMENTARY METHODS IN ANALYTIC NUMBER THEORY”, LENT 2015	2015	Adam J. Harper
+	LECTURE NOTES 0 FOR CAMBRIDGE PART III COURSE ON “ELEMENTARY METHODS IN ANALYTIC NUMBER THEORY”, LENT 2015	2015	Adam J. Harper
+	A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions	2015	Adam J. Harper Ashkan Nikeghbali Maksym Radziwiłł
+	Mean values of multiplicative functions over function fields	2015	Andrew Granville Adam J. Harper K. Soundararajan
+	Maxima of a randomized Riemann zeta function, and branching random walks	2015	Louis‐Pierre Arguin David Belius Adam J. Harper
+	A note on Helson's conjecture on moments of random multiplicative functions	2015	Adam J. Harper Ashkan Nikeghbali Maksym Radziwiłł
+	Orderings of weakly correlated random variables, and prime number races with many contestants	2015	Adam J. Harper Youness Lamzouri
+	Additive decompositions of sets with restricted prime factors	2014	Christian Elsholtz Adam J. Harper
+ PDF Chat	Inverse questions for the large sieve	2014	Ben Green Adam J. Harper
+	Pickands' constant $H_{\alpha}$ does not equal $1/\Gamma(1/\alpha)$, for small $\alpha$	2014	Adam J. Harper
+	LECTURE NOTES 2 FOR CAMBRIDGE PART III COURSE ON \THE RIEMANN ZETA FUNCTION", LENT 2014	2014	Adam J. Harper
+	LECTURE NOTES 0 FOR CAMBRIDGE PART III COURSE ON “THE RIEMANN ZETA FUNCTION”, LENT 2014	2014	Adam J. Harper
+	Pickands' constant $H_α$ does not equal $1/Γ(1/α)$, for small $α$	2014	Adam J. Harper
+	Inverse questions for the large sieve	2013	Ben J. Green Adam J. Harper
+	Additive decompositions of sets with restricted prime factors	2013	Christian Elsholtz Adam J. Harper
+	Sharp conditional bounds for moments of the Riemann zeta function	2013	Adam J. Harper
+ PDF Chat	Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function	2013	Adam J. Harper
+	A note on the maximum of the Riemann zeta function, and log-correlated random variables	2013	Adam J. Harper
+	Inverse questions for the large sieve	2013	Ben J. Green Adam J. Harper
+	Sharp conditional bounds for moments of the Riemann zeta function	2013	Adam J. Harper
+	Additive decompositions of sets with restricted prime factors	2013	Christian Elsholtz Adam J. Harper
+	Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers	2012	Adam J. Harper
+ PDF Chat	On the limit distributions of some sums of a random multiplicative function	2012	Adam J. Harper
+	Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers	2012	Adam J. Harper
+	On a paper of K. Soundararajan on smooth numbers in arithmetic progressions	2011	Adam J. Harper
+	On finding many solutions to S-unit equations by solving linear equations on average	2011	Adam J. Harper
+	On a paper of K. Soundararajan on smooth numbers in arithmetic progressions	2011	Adam J. Harper
+	On finding many solutions to S-unit equations by solving linear equations on average	2011	Adam J. Harper
+	On a paper of K. Soundararajan on smooth numbers in arithmetic progressions	2011	Adam J. Harper
+	On the limit distributions of some sums of a random multiplicative function	2010	Adam J. Harper
+	On the limit distributions of some sums of a random multiplicative function	2010	Adam J. Harper
+	Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations	2009	Adam J. Harper

Common Coauthors

Coauthor	Papers Together
K. Soundararajan	9
Youness Lamzouri	6
Andrew Granville	6
David Belius	3
Louis‐Pierre Arguin	3
Christian Elsholtz	3
Ashkan Nikeghbali	3
Maksym Radziwiłł	3
Kevin Ford	2
Ben J. Green	2
Kevin R. Ford	1
Ben Green	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan	10
+ PDF Chat	Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function	2013	Adam J. Harper	9
+ PDF Chat	Moments of the Riemann zeta function	2009	K. Soundararajan	8
+	Random factorizations and Riemann’s hypothesis	1944	Aurel Wintner	8
+	Multiplicative Number Theory	1980	H. Davenport	7
+	On mean values of random multiplicative functions	2012	Yuk-Kam Lau Gérald Tenenbaum Jie Wu	7
+ PDF Chat	Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition	2009	Gesine Reinert Adrian Röllin	6
+ PDF Chat	Random Multiplicative Functions in Short Intervals	2012	Sourav Chatterjee K. Soundararajan	6
+ PDF Chat	High moments of the Riemann zeta-function	2001	J. Brian Conrey S. M. Gonek	5
+	Opera de Cribro	2010	John Friedlander Henryk Iwaniec	5
+ PDF Chat	Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta Function	2012	Yan V. Fyodorov Ghaith A. Hiary Jonathan P. Keating	5
+	Summation of a random multiplicative function on numbers having few prime factors	2010	Bob Hough	5
+ PDF Chat	Freezing transitions and extreme values: random matrix theory, and disordered landscapes	2013	Yan V. Fyodorov Jonathan P. Keating	5
+	Probability: A Graduate Course	2012	Allan Gut	4
+	Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis	1994	Hugh L. Montgomery	4
+	Prime Number Races	2006	Andrew Granville Greg Martin	4
+ PDF Chat	The Shanks–Rényi prime number race with many contestants	2012	Youness Lamzouri	4
+ PDF Chat	Highly biased prime number races	2014	Daniel Fiorilli	4
+ PDF Chat	The maximum size of L-functions	2007	David W. Farmer S. M. Gonek C. P. Hughes	4
+ PDF Chat	HELSON'S PROBLEM FOR SUMS OF A RANDOM MULTIPLICATIVE FUNCTION	2015	Andriy Bondarenko Kristian Seip	4
+ PDF Chat	Integers, without large prime factors, in arithmetic progressions, I	1993	Andrew Granville	4
+ PDF Chat	Inequities in the Shanks–Rényi prime number race: An asymptotic formula for the densities	2012	Daniel Fiorilli Greg Martin	4
+ PDF Chat	Maxima of a randomized Riemann zeta function, and branching random walks	2017	Louis‐Pierre Arguin David Belius Adam J. Harper	4
+	Comparative prime number theory: A survey	2012	Greg Martin Justin Scarfy	4
+ PDF Chat	Decay of Mean Values of Multiplicative Functions	2003	Andrew Granville K. Soundararajan	4
+ PDF Chat	Prime number races with three or more competitors	2012	Youness Lamzouri	4
+ PDF Chat	A normal comparison inequality and its applications	2002	Wenbo V. Li Qi-Man Shao	4
+ PDF Chat	On integers free of large prime factors	1986	Adolf Hildebrand Gérald Tenenbaum	4
+ PDF Chat	The Spectrum of Multiplicative Functions	2001	Andrew Granville K. Soundararajan	3
+ PDF Chat	Hankel forms	2010	Henry Helson	3
+	Chebyshev's Bias	1994	Michael Rubinstein Peter Sarnak	3
+	A note on the maximum of the Riemann zeta function, and log-correlated random variables	2013	Adam J. Harper	3
+ PDF Chat	Primes in arithmetic progressions	1996	Olivier Ramaré Robert Rumely	3
+	Probability and Random Processes	2001	Geoffrey Grimmett David Stirzaker	3
+	Orderings of weakly correlated random variables, and prime number races with many contestants	2017	Adam J. Harper Youness Lamzouri	3
+ PDF Chat	Moments of random multiplicative functions, II: High moments	2019	Adam J. Harper	3
+	The Riemann Zeta-Function: Theory and Applications	2003	Aleksandar Ivić	3
+	MULTIPLICATIVE NUMBER THEORY	1970	Enrico Bombieri	3
+ PDF Chat	The distribution of the summatory function of the Möbius function	2004	Nathan Ng	3
+	Extrapolating the mean-values of multiplicative functions	1989	P. D. T. A. Elliott	3
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum	3
+ PDF Chat	Random Matrix Theory and ζ(1/2+ it)	2000	Jonathan P. Keating N. C. Snaith	3
+	The distribution of smooth numbers in arithmetic progressions	2008	K. Soundararajan	3
+ PDF Chat	Exact Asymptotics of the Freezing Transition of a Logarithmically Correlated Random Energy Model	2011	Christian Webb	3
+	On Λ(p)-subsets of squares	1989	Jean Bourgain	3
+	Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers	2012	Adam J. Harper	3
+	The inverse Goldbach problem	2001	Christian Elsholtz	3
+	Répartition Statistique Des Entiers Sans Grand Facteur Premier Dans Les Progressions Arithmétiques	1996	Étienne Fouvry Gérald Tenenbaum	3
+ PDF Chat	On the limit distributions of some sums of a random multiplicative function	2012	Adam J. Harper	3
+ PDF Chat	Quantitative mean value theorems for nonnegative multiplicative functions II	1987	Adolf Hildebrand	2