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The distribution of Hecke eigenvalues at Piatetski-Shapiro primes

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This is joint work with Liangyi Zhao. The distribution of Hecke eigenvalues at prime arguments has received a lot of attention. We are interested in the special question of how they are distributed at arguments from a certain sparse set of primes, namely Piatetski-Shapiro primes. The motivation for our investigation is two-fold. Firstly, the mean-values of arithmetic functions (in particular, of Fourier coefficients of cusp forms) over sparse sequences are often difficult to handle and thus of great interest. Secondly, it is a hard problem to detect primes in arithmetically interesting sets of natural numbers that are sparse. To tackle our problem, we are using a refinement of a method of Jutila to bound certain exponential sums with Fourier coefficients of cusp forms.

This talk is part of the Discrete Analysis Seminar series.

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