Algebraic twists of ${\mathrm{GL}}_3\times {\mathrm{GL}}_2$ $L$-functions

Abstract

We prove that the coefficients of a ${\mathrm{GL}}_3\times {\mathrm{GL}}_2$ Rankin--Selberg $L$-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result \cite{FKM1} for~${\mathrm{GL}}_2$ and \cite{KLMS} for ${\mathrm{GL}}_3$. This result is inspired by a recent work of P. Sharma who discussed the case of a Dirichlet character of prime modulus.

46 pages; final version; to appear in Amer. Journ. Math

Cited by in corpus (3)

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• Subconvexity for $GL(3)\times GL(2)$ twists (with an appendix by Will Sawin)
• Spectral aspect subconvex bounds for ${\mathrm{U}}_{n+1}\times {\mathrm{U}}_n$