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On the distribution of the divisor function and Hecke eigenvalues

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Stephen Lester & Nadav Yesha

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  1. Stephen Lester
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  2. Nadav Yesha
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Correspondence to Stephen Lester.

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Lester, S., Yesha, N. On the distribution of the divisor function and Hecke eigenvalues. Isr. J. Math. 212, 443–472 (2016). https://doi.org/10.1007/s11856-016-1290-0

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  • DOI: https://doi.org/10.1007/s11856-016-1290-0

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