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arXiv · 1110.4868

Multiple Dirichlet Series and Shifted Convolutions

Jeff Hoffstein·Thomas A. Hulse·Andre Reznikov
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Abstract

We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type bound for $L$-series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.

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Jeff Hoffstein, Thomas A. Hulse, Andre Reznikov. 2015-11-01. Multiple Dirichlet Series and Shifted Convolutions. https://arxiv.org/abs/1110.4868

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