Kernels for products of L-functions

Diamantis, Nikolaos; O’Sullivan, Cormac

doi:10.2140/ant.2013.7.1883

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Kernels for products of $L$-functions

Nikolaos Diamantis and Cormac O’Sullivan

Vol. 7 (2013), No. 8, 1883–1917

DOI: 10.2140/ant.2013.7.1883

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

Vol. 7, No. 8, 2013