Algebra & Number Theory

Kernels for products of $L$-functions

Nikolaos Diamantis and Cormac O’Sullivan

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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