#### Vol. 13, No. 6, 2019

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Weyl bound for $p$-power twist of $\mathrm{GL}(2)$ $L$-functions

### Ritabrata Munshi and Saurabh Kumar Singh

Vol. 13 (2019), No. 6, 1395–1413
DOI: 10.2140/ant.2019.13.1395
##### Abstract

Let $f$ be a cuspidal eigenform (holomorphic or Maass) for the congruence group ${\Gamma }_{0}\left(N\right)$ with $N$ square-free. Let $p$ be a prime and let $\chi$ be a primitive character of modulus ${p}^{3r}$. We shall prove the Weyl-type subconvex bound

$L\left(\frac{1}{2}+it,f\otimes \chi \right){\ll }_{f,t,\epsilon }{p}^{r+\epsilon },$

where $\epsilon >0$ is any positive real number.

##### Keywords
Maass forms, Hecke eigenforms, Voronoi summation formula, Poisson summation formula
##### Mathematical Subject Classification 2010
Primary: 11F66
Secondary: 11F55, 11M41