A+ CATEGORY SCIENTIFIC UNIT

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

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