A BESSEL DELTA METHOD AND EXPONENTIAL SUMS FOR GL(2)-Reference-Cited by-同舟云学术

A BESSEL DELTA METHOD AND EXPONENTIAL SUMS FOR GL(2)

Published:2020-07-08 Issue:3 Volume:71 Page:1143-1168
ISSN:0033-5606
Container-title:The Quarterly Journal of Mathematics
language:en
Short-container-title:

Author:

Aggarwal Keshav¹,Holowinsky Roman²,Lin Yongxiao³,Qi Zhi⁴

Affiliation:

1. Department of Mathematics and Statistics, The University of Maine, 5752 Neville Hall, Orono, ME 04469, USA

2. Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA

3. EPFL SB MATHGEOM TAN, Station 8, CH-1015, Lausanne, Switzerland

4. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

Abstract

Abstract In this paper, we introduce a simple Bessel $\delta $-method to the theory of exponential sums for $\textrm{GL}_2$. 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.

Funder

Deutsche Forschungsgemeinschaft

Swiss National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/qjmath/article-pdf/71/3/1143/33669719/haaa026.pdf

Reference38 articles.

1. Subconvexity bound for $\textrm{GL}(2)$${L}$-functions: ${t}$-aspect;Acharya;Acta Arith.,2020

2. Weyl bound for $\textrm{GL}(2)$ in ${t}$-aspect via a simple delta method;Aggarwal;J. Number Theory,2020