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Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 141, Number 5, October 2019
- pp. 1317-1345
- 10.1353/ajm.2019.0034
- Article
- Additional Information
abstract:
In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of ${\rm GL}_2$ or ${\rm GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for ${\rm GL}_2$ and the Miller type bound for ${\rm GL}_3$ which are uniform in terms of the additive character.