Commutation relations of Hecke operators for Arakawa lifting

Atsushi Murase, Hiroaki Narita

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

T. Arakawa, in his unpublished note, constructed and studied a theta lifting from elliptic cusp forms to automorphic forms on the quaternion unitary group of signature (1, q). The second named author proved that such a lifting provides bounded (or cuspidal) automorphic forms generating quaternionic discrete series. In this paper, restricting ourselves to the case of q = 1, we reformulate Arakawa's theta lifting as a theta correspondence in the adelic setting and determine a commutation relation of Hecke operators satisfied by the lifting. As an application, we show that the theta lift of an elliptic Hecke eigenform is also a Hecke eigenform on the quaternion unitary group. We furthermore study the spinor L-function attached to the theta lift.

Original languageEnglish
Pages (from-to)227-251
Number of pages25
JournalTohoku Mathematical Journal
Volume60
Issue number2
DOIs
Publication statusPublished - 2008 Jun 1
Externally publishedYes

    Fingerprint

Keywords

  • Hecke operators
  • Spinor L-functions
  • Theta lifting

ASJC Scopus subject areas

  • Mathematics(all)

Cite this