Vol. 7, No. 8, 2013

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Kernels for products of $L$-functions

Nikolaos Diamantis and Cormac O’Sullivan

Vol. 7 (2013), No. 8, 1883–1917
Abstract

The Rankin–Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their nonholomorphic analogs and show their connection to values of L-functions outside the critical strip.

Keywords
$L$-functions, noncritical values, Rankin–Cohen brackets, Eichler–Shimura–Manin theory
Mathematical Subject Classification 2010
Primary: 11F67
Secondary: 11F03, 11F37
Milestones
Received: 30 May 2012
Accepted: 21 December 2012
Published: 24 November 2013
Authors
Nikolaos Diamantis
School of Mathematical Sciences
University of Nottingham
University Park
Nottingham NG7 2RD
United Kingdom
Cormac O’Sullivan
Department of Mathematics
The City University of New York Graduate Center
365 Fifth Avenue
New York, NY 10016-4309
United States