Explicit doubling integrals for using ``good test vectors''
Author:
Christian A. Zorn
Journal:
Represent. Theory 14 (2010), 285323
MSC (2010):
Primary 22E50; Secondary 11F70
Published electronically:
March 15, 2010
MathSciNet review:
2608965
Fulltext PDF Free Access
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Additional Information
Abstract: In a previous paper (see http:/www.math.ohiostate.edu/~czorn/works.html), we computed examples of the doubling integral for constituents of the unramified principal series of and where was a nondyadic field. These computations relied on certain ``good test vectors'' and ``good theta test sections'' motivated by the nonvanishing of theta lifts. In this paper, we aim to prove a partial analog for . However, due to several complexities, we compute the doubling integral only for certain irreducible principal series representations induced from characters with ramified quadratic twists. We develop some adic analogs for the machinery in the paper mentioned above; however, these tend to be more delicate and have more restrictive hypotheses than the nondyadic case. Ultimately, this paper and the one mentioned above develop several computations intended to be used for future research into the nonvanishing of theta lifts.
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Additional Information
Christian A. Zorn
Affiliation:
Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, Ohio 43210
Email:
czorn@math.ohiostate.edu
DOI:
http://dx.doi.org/10.1090/S1088416510003717
PII:
S 10884165(10)003717
Received by editor(s):
January 9, 2009
Received by editor(s) in revised form:
December 7, 2009
Published electronically:
March 15, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
