Average of Dirichlet Coefficients of Cuspidal Representations Related to $\GL(2)$

Liyang Yang

Average of Dirichlet Coefficients of Cuspidal Representations Related to $\GL(2)$

Number Theory 2019-11-11 v2

Authors: Liyang Yang

Abstract

Let $\pi$ be a cuspidal representation on $\GL(2,\mathbb{A}_{\mathbb{Q}}).$ We give nontrivial lower and upper bounds for average of absolute values of Dirichlet coefficients associated to $\pi;$ and nontrivial upper bound in the case of $\Sym^k\pi,$ $k=2, 3.$ These bounds generalize the known estimates in holomorphic case to Maass forms, without assuming Ramanujan-Petersson conjecture.

Keywords

cuspidal representations dirichlet coefficients gl(2) maass forms average bounds symmetric powers

Cite

@article{arxiv.1911.02148,
  title  = {Average of Dirichlet Coefficients of Cuspidal Representations Related to $\GL(2)$},
  author = {Liyang Yang},
  journal= {arXiv preprint arXiv:1911.02148},
  year   = {2019}
}

Comments

24 pages; some typos are fixed

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