Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 1 (2013), 117-155.
$L$-functions and periods of adjoint motives
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 -functions. When the automorphic representations are of motivic type, it is shown that the -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) -functions.
Algebra Number Theory, Volume 7, Number 1 (2013), 117-155.
Received: 10 July 2011
Revised: 12 October 2011
Accepted: 20 February 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 11G09: Drinfelʹd modules; higher-dimensional motives, etc. [See also 14L05]
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