Geodesic
Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms
Shingo Sugiyama 1   ; Masao Tsuzuki 2
1 Institute of Mathematics for Industry Kyushu University 744, Motooka, Nishi-ku Fukuoka 819-0395, Japan
2 Department of Science and Technology Sophia University Kioi-cho 7-1, Chiyoda-ku Tokyo 102-8554, Japan
Acta Arithmetica, Tome 176 (2016) no. 1, pp. 1-63 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa8021-4-2016
Keywords: elaborate explicit version relative trace formula pgl totally real number field toral periods hilbert cusp forms along diagonal split torus application prove spectral equidistribution result level aspect satake parameters holomorphic hilbert cusp forms weighted central l values bound quadratic base change l functions hilbert cusp forms subconvex exponent weight aspect

Shingo Sugiyama  1   ; Masao Tsuzuki  2

1 Institute of Mathematics for Industry Kyushu University 744, Motooka, Nishi-ku Fukuoka 819-0395, Japan
2 Department of Science and Technology Sophia University Kioi-cho 7-1, Chiyoda-ku Tokyo 102-8554, Japan 
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     title = {Relative trace formulas and subconvexity estimates for $L$-functions of {Hilbert} modular forms},
     journal = {Acta Arithmetica},
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Shingo Sugiyama; Masao Tsuzuki. Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms. Acta Arithmetica, Tome 176 (2016) no. 1, pp. 1-63. doi: 10.4064/aa8021-4-2016

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