PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms

Volume 166 / 2014

Yujiao Jiang, Guangshi Lü Acta Arithmetica 166 (2014), 231-252 MSC: 11F30, 11F66. DOI: 10.4064/aa166-3-2

Abstract

Let $\lambda_f(n)$ be the $n$th normalized Fourier coefficient of a holomorphic or Maass cusp form $f$ for $\mathrm{SL(2,\mathbb{Z})}$. We establish the asymptotic formula for the summatory function $$ \sum_{\substack{n\leq x \\ n\equiv l \,({\rm mod}\, q)}}|\lambda_f(n)|^{2j} $$ as $x\rightarrow \infty,$ where $q$ grows with $x$ in a definite way and $j=2,3,4$.

Authors

  • Yujiao JiangDepartment of Mathematics
    Shandong University
    Jinan, Shandong, 250100, China
    e-mail
  • Guangshi LüDepartment of Mathematics
    Shandong University
    Jinan, Shandong, 250100, China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image