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arXiv · 1305.2261

Relative trace formulas and subconvexity estimates of L-functions for Hilbert modular forms

Shingo Sugiyama·Masao Tsuzuki
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Abstract

We elaborate an explicit version of the relative trace formula on $\PGL(2)$ over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split torus. As an application, we prove (i) a spectral equidistribution result in the level aspect for Satake parameters of holomorphic Hilbert cusp forms weighted by central $L$-values, and (ii) a bound of quadratic base change $L$-functions for Hilbert cusp forms with a subconvex exponent in the weight aspect.

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Shingo Sugiyama, Masao Tsuzuki. 2013-05-10. Relative trace formulas and subconvexity estimates of L-functions for Hilbert modular forms. https://doi.org/10.1215/21562261-2017-0025

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