Abstract
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.
Original language | English |
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Pages (from-to) | 137-185 |
Number of pages | 49 |
Journal | Nagoya Mathematical Journal |
Volume | 222 |
DOIs | |
Publication status | Published - 2016 Jun 1 |
Keywords
- 2010 Mathematics subject classification 11F55 11F70
ASJC Scopus subject areas
- Mathematics(all)