  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.

Number Theory;Algebraic Geometry