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

Volume 176 / 2016

Shingo Sugiyama, Masao Tsuzuki Acta Arithmetica 176 (2016), 1-63 MSC: Primary 11F67; Secondary 11F72. DOI: 10.4064/aa8021-4-2016 Published online: 10 October 2016


We elaborate an explicit version of the relative trace formula on ${\rm PGL}(2)$ 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 on quadratic base change $L$-functions for Hilbert cusp forms with a subconvex exponent in the weight aspect.


  • Shingo SugiyamaInstitute of Mathematics for Industry
    Kyushu University
    744, Motooka, Nishi-ku
    Fukuoka 819-0395, Japan
  • Masao TsuzukiDepartment of Science and Technology
    Sophia University
    Kioi-cho 7-1, Chiyoda-ku
    Tokyo 102-8554, Japan

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