Triple divisor type functions in arithmetic progressions to prime power moduli

Abstract

We study the equidistribution in arithmetic progressions modulo powers of a fixed odd prime of Hecke eigenvalues of noncuspidal $\mathrm{GL}_3$ automorphic forms, with a focus on the convolution coefficients $\lambda_{1\boxplus f}(n)=(\lambda_f\star 1)(n)$,attached to a level $1$ holomorphic primitive cusp form $f$. Utilizing techniques introduced by Kowalski--Lin--Michel and Mili\'{c}evi\'{c}, we prove the exponent $\vartheta=1/2+7/458-\varepsilon$ is admissible.