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)

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arxiv 1906.05485 v4 pith:MCHOPUC2 submitted 2019-06-13 math.NT

Keshav Aggarwal , Roman Holowinsky , Yongxiao Lin , Zhi Qi This is my paper · ORCID

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keywords exponentialsumsbesselarbitraryaspectassociatedbounddelta

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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.

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