## Algebra & Number Theory

### $L$-functions and periods of adjoint motives

Michael Harris

#### Abstract

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.

#### Article information

Source
Algebra Number Theory, Volume 7, Number 1 (2013), 117-155.

Dates
Revised: 12 October 2011
Accepted: 20 February 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729931

Digital Object Identifier
doi:10.2140/ant.2013.7.117

Mathematical Reviews number (MathSciNet)
MR3037892

Zentralblatt MATH identifier
1319.11028

#### Citation

Harris, Michael. $L$-functions and periods of adjoint motives. Algebra Number Theory 7 (2013), no. 1, 117--155. doi:10.2140/ant.2013.7.117. https://projecteuclid.org/euclid.ant/1513729931

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