Algebraic twists of GL3 × GL2 L-functions

Abstract

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