"Beyond the Weyl barrier for GL(2) exponential sums" by Roman Holowinsky, Ritabrata Munshi et al.
 

Beyond the Weyl barrier for GL(2) exponential sums

Article Type

Research Article

Publication Title

Advances in Mathematics

Abstract

In this paper, we use the Bessel δ-method, along with new variants of the van der Corput method in two dimensions, to prove non-trivial bounds for GL(2) exponential sums beyond the Weyl barrier. More explicitly, for sums of GL(2) Fourier coefficients twisted by e(f(n)), with length N and phase f(n)=Nβlog⁡n/2π or anβ, non-trivial bounds are established for β<1.63651..., which is beyond the Weyl barrier at β=3/2.

DOI

https://10.1016/j.aim.2023.109099

Publication Date

8-1-2023

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