On Hecke Eigenvalues at Piatetski-Shapiro Primes

Details On Hecke Eigenvalues at Piatetski-Shapiro Primes On Hecke Eigenvalues at Piatetski-Shapiro Primes

2008-08-12

arxiv.org/abs/0808.1756v3

J. London Math. Soc. (2), Vol. 81, 2010, No. 1, pp. 175-201.

Mathematics

Number Theory

24 pages, with updated reference and minor revisions

Scientific paper

Let $\lambda(n)$ be the normalized n-th Fourier coefficient of a holomorphic cusp form for the full modular group. We show that for some constant $C > 0$ depending on the cusp form and every fixed $c$ in the range $1 < c < 8/7$, the mean value of $\lambda(p)$ is $\ll \exp (-C \sqrt{\log N})$ as p runs over all (Piatetski-Shapiro) primes of the form $[n^c]$ with a natural number $n \leq N$.

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