On the distribution of the divisor function and Hecke eigenvalues

Stephen Lester; Nadav Yesha

doi:10.1007/s11856-016-1290-0

On the distribution of the divisor function and Hecke eigenvalues

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by É. Fouvry, S. Ganguly, E. Kowalski and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.

Original language	American English
Pages (from-to)	443-472
Number of pages	30
Journal	Israel Journal of Mathematics
Volume	212
Issue number	1
DOIs	https://doi.org/10.1007/s11856-016-1290-0
State	Published - 1 May 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-016-1290-0

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AU - Yesha, Nadav

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AB - We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by É. Fouvry, S. Ganguly, E. Kowalski and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.

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DO - 10.1007/s11856-016-1290-0

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

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On the distribution of the divisor function and Hecke eigenvalues

Abstract

All Science Journal Classification (ASJC) codes

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