Cancellation in the Additive Twists of Fourier Coefficients for ${\mathrm{GL}}_2$ and ${\mathrm{GL}}_3$ over Number Fields

Abstract

In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of ${\mathrm{GL}}_2$ or ${\mathrm{GL}}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for ${\mathrm{GL}}_2$ and the Miller type bound for ${\mathrm{GL}}_3$ which are uniform in terms of the additive character.

23 pages. Corrected the translation of Voronoi (the different ideal was missing)

References in corpus (1)

• Theory of Fundamental Bessel Functions of High Rank

Cited by in corpus (2)

• Subconvexity for twisted $L$-functions on ${\mathrm{GL}}_3$ over the Gaussian number field
• Bessel Identities in the Waldspurger Correspondence over the Complex Numbers