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

Brooke Feigon, David Whitehouse
2009 Duke mathematical journal  
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 Lvalues. Corollary 1.3. Let F = Q and J ⊂ [−2, +2]. Then lim N →∞ 1 |F(N, 2k)| π∈F (N,2k) ap(π)∈J
doi:10.1215/00127094-2009-041 fatcat:2pazkpyt5jcptofbtkntr37bfy