Special values of shifted convolution Dirichlet series

Abstract

In a recent important paper, Hoffstein and Hulse generalized the notion of Rankin-Selberg convolution $L$-functions by defining shifted convolution $L$-functions. We investigate symmetrized versions of their functions. Under certain mild conditions, we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and "mixed mock modular" forms.

18 pages, corrected slight error in main theorem and made according minor edits in Sections 3.4 and 3.5

Cited by in corpus (1)

• Eichler-Selberg Type Identities for Mixed Mock Modular Forms