Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hoffstein, Jeff, Hulse, Thomas A., Reznikov, Andre
Institutions: Brown University, Colby College, Bar-Ilan University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951249972