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2013 $L$-functions and periods of adjoint motives
Michael Harris
Algebra Number Theory 7(1): 117-155 (2013). DOI: 10.2140/ant.2013.7.117


The article studies the compatibility of the refined Gross–Prasad (or Ichino–Ikeda) conjecture for unitary groups, due to Neal Harris, with Deligne’s conjecture on critical values of L-functions. When the automorphic representations are of motivic type, it is shown that the L-values that arise in the formula are critical in Deligne’s sense, and their Deligne periods can be written explicitly as products of Petersson norms of arithmetically normalized coherent cohomology classes. In some cases this can be used to verify Deligne’s conjecture for critical values of adjoint type (Asai) L-functions.


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Michael Harris. "$L$-functions and periods of adjoint motives." Algebra Number Theory 7 (1) 117 - 155, 2013.


Received: 10 July 2011; Revised: 12 October 2011; Accepted: 20 February 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1319.11028
MathSciNet: MR3037892
Digital Object Identifier: 10.2140/ant.2013.7.117

Primary: 11F67
Secondary: 11F70 , 11G09 , 14G35

Keywords: adjoint $L$-functions , automorphic forms , Ichino–Ikeda conjecture , motives , periods

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 1 • 2013
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