Bounds for short character sums for $GL(2)\times GL(3)$ twists

Abstract

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke Maass-cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass-cusp form with normalized Fourier coefficients ${\lambda }_{\pi }(r,n)\text{ and }{\lambda }_f(n)$ respectively and $\chi$ be any non-trivial character mod $p$ where $p$ is a prime. Then we have $$S_{\pi ,f,\chi }(N){\ll }_{\pi ,f,\epsilon }{N}^{3/4}{p}^{11/16+\eta /4}(Np{)}^{\epsilon }.$$

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References in corpus (1)

• Weyl-type bounds for twisted $GL(2)$ short character sums