Special values of shifted convolution Dirichlet series

Mertens, Michael H and Ono, Ken Special values of shifted convolution Dirichlet series. Mathematika, 62. 47 - 66.

Text
1406.0770v4.pdf - Accepted Version
Download (261kB) | Preview

Official URL: http://dx.doi.org/10.1112/S0025579315000169

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.

Item Type:	Article
Additional Information:	18 pages, corrected slight error in main theorem and made according minor edits in Sections 3.4 and 3.5
Uncontrolled Keywords:	math.NT, math.NT, 11F37, 11G40, 11G05, 11F67
Depositing User:	Symplectic Admin
Date Deposited:	01 Jul 2020 08:46
Last Modified:	01 Jul 2020 08:46
DOI:	10.1112/S0025579315000169
Related URLs:	Author Publisher
URI:	http://livrepository.liverpool.ac.uk/id/eprint/3092363