Period relations for automorphic forms on unitary groups and critical values of $L$-functions

Lucio Guerberoff

Period relations for automorphic forms on unitary groups and critical values of $L$-functions

Number Theory 2016-12-20 v4

Authors: Lucio Guerberoff

Abstract

In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$ -functions. We prove a formula expressing the critical values in the range of absolute convergence in terms of Petersson norms of holomorphic automorphic forms. On the other hand, we express the Deligne period of a related motive as a product of quadratic periods and compare the two expressions by means of Deligne's conjecture.

Keywords

automorphic forms unitary groups cm fields l-functions critical values period relations deligne conjecture

Cite

@article{arxiv.1512.03867,
  title  = {Period relations for automorphic forms on unitary groups and critical values of $L$-functions},
  author = {Lucio Guerberoff},
  journal= {arXiv preprint arXiv:1512.03867},
  year   = {2016}
}

Comments

51 pages; incorporated referee comments

Period relations for automorphic forms on unitary groups and critical values of $L$-functions

Abstract

Keywords

Cite

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