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

Abstract

In this paper, we introduce a simple Bessel $\hat{I}´$-method to the theory of exponential sums for $\mathrm{G}{\mathrm{L}}_2$. 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.

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