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International Mathematics Research Notices Advance Access originally published online on December 25, 2008
International Mathematics Research Notices (2009) 2009:141-191, doi:10.1093/imrn/rnn127 published on January 9, 2009
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org.

Central L-Values and Toric Periods for GL(2)

Kimball Martin1 and David Whitehouse2

1 Columbia University, Department of Mathematics, 2990 Broadway, Mailcode 4406, New York, NY 10027, USA
2 School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA

Correspondence: Correspondence to be sent to: kmartin{at}math.ou.edu

Let {pi} be a cusp form on GL(2) over a number field F and let E be a quadratic extension of F. Denote by {pi}E the base change of {pi} to E and by {Omega} a unitary character of AxE/ Ex. We use the relative trace formula to give an explicit formula for L(1/2, {pi}E {otimes} {Omega}) in terms of period integrals of Gross–Prasad test vectors. We give an application of this formula to equidistribution of geodesics on a hyperbolic 3-fold.


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