Commutation relations of Hecke operators for Arakawa lifting

Atsushi Murase*, Hiro Aki Narita

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


T. Arakawa, in his unpublished note, constructed and studied a theta lifting from elliptic cusp forms to automorphic forms on the quaternion unitary group of signature (1, q).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
Issue number2
Publication statusPublished - 2008 Jun
Externally publishedYes


  • Hecke operators
  • Spinor L-functions
  • Theta lifting

ASJC Scopus subject areas

  • General Mathematics


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