Triple divisor type functions in arithmetic progressions to prime power moduli

Source 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 $λ_{1\boxplus f}(n)=(λ_f\star 1)(n)$,attached to a level $1$ holomorphic primitive cusp form $f$. Utilizing techniques introduced by Kowalski--Lin--Michel and Milićević, we prove the exponent $\vartheta=1/2+7/458-\varepsilon$ is admissible.