Averages of central L -values of Hilbert modular forms with an application to subconvexity

We use the relative trace formula to obtain exact formulas for central values of certain twisted quadratic base change L -functions averaged over Hilbert modular forms of a fixed weight and level. We apply these formulas to the subconvexity problem for these L -functions. We also establish an equidi...

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Bibliographic Details
Published in:Duke mathematical journal 2009-08, Vol.149 (2), p.347-410
Main Authors: Feigon, Brooke, Whitehouse, David
Format: Article
Language:English
Subjects:
11F66
11F67
11F70
11F72
11M41
11R52
11S40
11S45
cohomology
for algebro-geometric methods
modular symbols
Other Dirichlet series and zeta functions {For local and global ground fields
periods of modular forms
see 11R42
see 14G10
see also 11E45
Selberg trace formula
Special values of automorphic $L$-series
Spectral theory
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Summary:We use the relative trace formula to obtain exact formulas for central values of certain twisted quadratic base change L -functions averaged over Hilbert modular forms of a fixed weight and level. We apply these formulas to the subconvexity problem for these L -functions. We also establish an equidistribution result for the Hecke eigenvalues weighted by these L -values
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2009-041