Multiple Dirichlet Series and Shifted Convolutions
Number Theory
2015-11-03 v6
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 -series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.
Cite
@article{arxiv.1110.4868,
title = {Multiple Dirichlet Series and Shifted Convolutions},
author = {Jeff Hoffstein and Thomas A. Hulse and Andre Reznikov},
journal= {arXiv preprint arXiv:1110.4868},
year = {2015}
}