Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms
Acta Arithmetica, Tome 176 (2016) no. 1, pp. 1-63
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Shingo Sugiyama 1 ; Masao Tsuzuki 2
@article{10_4064_aa8021_4_2016,
author = {Shingo Sugiyama and Masao Tsuzuki},
title = {Relative trace formulas and subconvexity estimates for $L$-functions of {Hilbert} modular forms},
journal = {Acta Arithmetica},
pages = {1--63},
publisher = {mathdoc},
volume = {176},
number = {1},
year = {2016},
doi = {10.4064/aa8021-4-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8021-4-2016/}
}
TY - JOUR AU - Shingo Sugiyama AU - Masao Tsuzuki TI - Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms JO - Acta Arithmetica PY - 2016 SP - 1 EP - 63 VL - 176 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8021-4-2016/ DO - 10.4064/aa8021-4-2016 LA - en ID - 10_4064_aa8021_4_2016 ER -
%0 Journal Article %A Shingo Sugiyama %A Masao Tsuzuki %T Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms %J Acta Arithmetica %D 2016 %P 1-63 %V 176 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa8021-4-2016/ %R 10.4064/aa8021-4-2016 %G en %F 10_4064_aa8021_4_2016
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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