An alternative development of analytic number theory and applications

Publications

Peer reviewed articles (14)

Planck-Scale Mass Equidistribution of Toral Laplace Eigenfunctions

Author(s): Granville, A.; Wigman, I.
Published in: Communications in Mathematical Physics , 355 (2) pp. 767-802. (2017), 1, 2017, ISSN 0010-3616
Publisher: Springer Verlag

A more intuitive proof of a sharp version of Halász’s theorem

Author(s): Andrew Granville, Adam J. Harper, K. Soundararajan
Published in: Proceedings of the American Mathematical Society, 2018, Page(s) 1, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/14095

SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE -BARRIER

Author(s): Sary Drappeau, Andrew Granville, Xuancheng Shao
Published in: Mathematika, 63/03, 2017, Page(s) 895-918, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/S0025579317000225

Large character sums: Burgess's theorem and zeros of $L$-functions

Author(s): Andrew Granville, Kannan Soundararajan
Published in: Journal of the European Mathematical Society, 20/1, 2018, Page(s) 1-14, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/JEMS/757

Beyond the LSD method for the partial sums of multiplicative functions

Author(s): Granville, Andrew; Koukoulopoulos, Dimitris
Published in: Ramanujan Journal, 2, 2019, ISSN 1382-4090
Publisher: Kluwer Academic Publishers

A new proof of Hal\'asz's Theorem, and its consequences

Author(s): Granville, Andrew; Harper, Adam J; Soundararajan, K.
Published in: Compositio Mathematica, 5, 2019, ISSN 0010-437X
Publisher: London Mathematical Society

Spins of prime ideals and the negative Pell equation

Author(s): P. Koymans, D. Z. Milovic
Published in: Compositio Mathematica, 155/1, 2019, Page(s) 100-125, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/S0010437X18007601

Motohashi’s fourth moment identity for non-archimedean test functions and applications

Author(s): Valentin Blomer, Peter Humphries, Rizwanur Khan, Micah B. Milinovich
Published in: Compositio Mathematica, 156/5, 2020, Page(s) 1004-1038, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/S0010437X20007101

Standard zero-free regions for Rankin–Selberg L-functions via sieve theory

Author(s): Peter Humphries, Farrell Brumley
Published in: Mathematische Zeitschrift, 292/3-4, 2019, Page(s) 1105-1122, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-018-2136-8

A note on the maximum of the Riemann zeta function on the 1-line

Author(s): Heap, Winston
Published in: Bulletin LMS, 5, 2020, ISSN 1469-2120
Publisher: London Mathematical Society
DOI: 10.1112/blms.12382

SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION

Author(s): Winston Heap, Maksym Radziwiłł, K Soundararajan
Published in: The Quarterly Journal of Mathematics, 70/4, 2019, Page(s) 1387-1396, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmathj/haz027

A new proof of Halász’s theorem, and its consequences

Author(s): Andrew Granville, Adam J. Harper, K. Soundararajan
Published in: Compositio Mathematica, 155/1, 2019, Page(s) 126-163, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/S0010437X18007522

WHEN DOES THE BOMBIERI–VINOGRADOV THEOREM HOLD FOR A GIVEN MULTIPLICATIVE FUNCTION?

Author(s): ANDREW GRANVILLE, XUANCHENG SHAO
Published in: Forum of Mathematics, Sigma, 6, 2018, ISSN 2050-5094
Publisher: Cambridge
DOI: 10.1017/fms.2018.14

Bombieri-Vinogradov for multiplicative functions, and beyond the x1/2-barrier

Author(s): Andrew Granville, Xuancheng Shao
Published in: Advances in Mathematics, 350, 2019, Page(s) 304-358, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2019.04.055

Other (1)

The frequency and the structure of large character sums

Author(s): Jonathan Bober, Leo Goldmakher, Andrew Granville, Dimitris Koukoulopoulos
Published in: Journal of the European Mathematical Society, 2017
Publisher: EMS