On Hecke eigenvalues at Piatetski-Shapiro primes

On Hecke eigenvalues at Piatetski-Shapiro primes

Let λ(n) be the normalized nth 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 λ(p) is as p runs over all (Piatetski-Shapiro) primes of t...

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Bibliographic Details
Main Authors: Baier, Stephan, Zhao, Liangyi
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2011
Subjects:
DRNTU::Science::Mathematics::Number theory
Online Access:https://hdl.handle.net/10356/93859
http://hdl.handle.net/10220/7064
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Institution: Nanyang Technological University
Language: English
Description
Summary:Let λ(n) be the normalized nth 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 λ(p) is as p runs over all (Piatetski-Shapiro) primes of the form [nc] with n ∈ ℕ and n ≤ N.

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