Algebra & Number Theory

Kernels for products of $L$-functions

Nikolaos Diamantis and Cormac O’Sullivan

Full-text: Open access

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.

Article information

Source
Algebra Number Theory, Volume 7, Number 8 (2013), 1883-1917.

Dates
Received: 30 May 2012
Accepted: 21 December 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730072

Digital Object Identifier
doi:10.2140/ant.2013.7.1883

Mathematical Reviews number (MathSciNet)
MR3134038

Zentralblatt MATH identifier
1286.11077

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F03: Modular and automorphic functions 11F37: Forms of half-integer weight; nonholomorphic modular forms

Keywords
$L$-functions noncritical values Rankin–Cohen brackets Eichler–Shimura–Manin theory

Citation

Diamantis, Nikolaos; O’Sullivan, Cormac. Kernels for products of $L$-functions. Algebra Number Theory 7 (2013), no. 8, 1883--1917. doi:10.2140/ant.2013.7.1883. https://projecteuclid.org/euclid.ant/1513730072


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