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arXiv · 1409.3797

Character sums of composite moduli and hybrid subconvexity

Roman Holowinsky·Ritabrata Munshi·Zhi Qi
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Abstract

Let $M=M_1 M_2 M_3$ be the product of three distinct primes and let $\chi=\chi_1 \chi_2 \chi_3$ be a Dirichlet character of modulus $M$ such that each $\chi_i$ is a primitive character modulo $M_i$ for $i=1,2,3$. In this paper, we provide a $\delta$-symbol method for obtaining non-trivial cancellation in smooth character sums of the form $\sum_{n=1}^\infty \chi(n) W(n/N)$, with $N$ roughly of size $\sqrt M$ and $W$ a smooth compactly supported weight function on $(0, \infty)$. As a corollary, we establish hybrid subconvexity bounds for the associated Dirichlet $L$-function.

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Roman Holowinsky, Ritabrata Munshi, Zhi Qi. 2014-09-12. Character sums of composite moduli and hybrid subconvexity. https://arxiv.org/abs/1409.3797

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