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SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  16 June 2015

Michael H. Mertens  and
Ken Ono
Michael H. Mertens
Affiliation:
Mathematisches Institut der Universität zu Köln, Weyertal 86–90, D-50931 Köln, Germany email mmertens@math.uni-koeln.de
Ken Ono
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30022, U.S.A. email ono@mathcs.emory.edu
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Abstract

In a recent important paper, Hoffstein and Hulse [Multiple Dirichlet series and shifted convolutions, arXiv:1110.4868v2] generalized the notion of Rankin–Selberg convolution $L$-functions by defining shifted convolution$L$-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

MSC classification

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G05: Elliptic curves over global fields 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 1 , 2016 , pp. 47 - 66
Copyright
Copyright © University College London 2015 

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