Lifting to GL(2) over a division quaternion algebra, and an explicit construction of cap representations

Masanori Muto, Hiro Aki Narita, Ameya Pitale

研究成果: Article査読

4 被引用数 (Scopus)

抄録

The aim of this paper is to carry out an explicit construction of CAP representations of over a division quaternion algebra with discriminant two. We first construct cusp forms on such a group explicitly by lifting from Maass cusp forms for the congruence subgroup . We show that this lifting is nonzero and Hecke-equivariant. This allows us to determine each local component of a cuspidal representation generated by such a lifting. We then show that our cuspidal representations provide examples of CAP (cuspidal representation associated to a parabolic subgroup) representations, and, in fact, counterexamples to the Ramanujan conjecture.

本文言語English
ページ(範囲)137-185
ページ数49
ジャーナルNagoya Mathematical Journal
222
DOI
出版ステータスPublished - 2016 6月 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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