On Hecke eigenvalues at Piatetski-Shapiro primes
Date of Issue2010
School of Physical and Mathematical Sciences
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.
Journal of the London mathematical society
© 2009 London Mathematical Society. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of the London mathematical society, London Mathematical Society. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1112/jlms/jdp064].