Multiple Dirichlet Series and Shifted Convolutions

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.

References in corpus (1)

• Shifted Multiple Dirichlet Series

Cited by in corpus (6)

• Subconvexity for Half Integral Weight $L$-functions
• Second Moments and simultaneous non-vanishing of GL(2) automorphic L-series
• On Some Variants of the Gauss Circle Problem
• The Second Moment of Sums of Coefficients of Cusp Forms
• Shifted Multiple Dirichlet Series
• Shifted convolution sums and Eisenstein series formed with modular symbols