A Bessel delta-method and exponential sums for GL(2)

Keshav Aggarwal; Roman Holowinsky; Yongxiao Lin; Zhi Qi

A Bessel delta-method and exponential sums for GL(2)

Number Theory 2020-05-14 v4

Authors: Keshav Aggarwal , Roman Holowinsky , Yongxiao Lin , Zhi Qi

Abstract

In this paper, we introduce a simple Bessel $\delta$ -method to the theory of exponential sums for $\rm GL_2$ . Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and nebentypus. In particular, this gives a short proof for the Weyl-type subconvex bound in the $t$ -aspect for the associated $L$ -functions.

Keywords

exponential sums zeta values and euler sums l-functions

Cite

@article{arxiv.1906.05485,
  title  = {A Bessel delta-method and exponential sums for GL(2)},
  author = {Keshav Aggarwal and Roman Holowinsky and Yongxiao Lin and Zhi Qi},
  journal= {arXiv preprint arXiv:1906.05485},
  year   = {2020}
}

Comments

new title; major changes; results extended and strengthened; the text arXiv:1906.06371 has been merged into this paper; 20 pages; accepted by Q. J. Math

A Bessel delta-method and exponential sums for GL(2)

Abstract

Keywords

Cite

Comments

Related papers