@article{db4b601ec4b24d84908985786c77e6fd,
title = "Lifting to GL(2) over a division quaternion algebra, and an explicit construction of cap representations",
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.",
keywords = "2010 Mathematics subject classification 11F55 11F70",
author = "Masanori Muto and Narita, {Hiro Aki} and Ameya Pitale",
note = "Funding Information: Received June 21, 2014. Accepted June 11, 2015. 2010 Mathematics subject classification. 11F55, 11F70. The second author was partly supported by Grant-in-Aid for Scientific Research (C) 24540025, Japan Society for the Promotion of Science. The third author was partly supported by National Science Foundation grant DMS-1100541. Publisher Copyright: {\textcopyright} 2016 by The Editorial Board of the Nagoya Mathematical Journal.",
year = "2016",
month = jun,
day = "1",
doi = "10.1017/nmj.2016.15",
language = "English",
volume = "222",
pages = "137--185",
journal = "Nagoya Mathematical Journal",
issn = "0027-7630",
publisher = "Nagoya University",
}