A BESSEL DELTA METHOD AND EXPONENTIAL SUMS FOR GL(2). (8th July 2020)

• Record Type: Journal Article
• Authors: Aggarwal, Keshav; Holowinsky, Roman; Lin, Yongxiao; Qi, Zhi
• Is Part Of: Quarterly journal of mathematics. Volume 71:Part 3(2020)
• Page Start: 1143
• Page End: 1168
• Publication Date: 2020-07-08
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmathj/haaa026
• Languages: English
• ISSNs: 0033-5606

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.