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.
A coordinated search for flares from the dMe star YZ Canis Minoris was performed in 1979 October using the Einstein Observatory and ground-based optical and radio telescopes. An event was detected in the optical, radio, and X-ray wavebands on October 25, and a second optical event on October 27 was seen as a marginal (2
We give a method to explicitly determine the space of unramified Hilbert cusp forms of weight two, together with the action of Hecke, over a totally real number field of even degree and narrow class number one. In particular, one can determine the eigenforms in this space and compute their Hecke eigenvalues to any reasonable degree. As an application we compute this space of cusp forms for (ޑ √ 509), and determine each eigenform in this space which has rational Hecke eigenvalues. We find that not all of these forms arise via base change from classical forms. To each such eigenform f we attach an elliptic curve with good reduction everywhere whose L-function agrees with that of f at every place.
Let π be a cuspidal automorphic representation of PGL(2n) over a number field F , and η the quadratic idèle class character attached to a quadratic extension E/F . Guo and Jacquet conjectured a relation between the nonvanishing of L(1/2, π)L(1/2, π⊗ η) for π of symplectic type and the nonvanishing of certain GL(n, E) periods. When n = 1, this specializes to a well-known result of Waldspurger. We prove this conjecture, and related global results, under some local hypotheses using a simple relative trace formula.We then apply these global results to obtain local results on distinguished supercuspidal representations, which partially establish a conjecture of Prasad and Takloo-Bighash.
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