Geodesic
Existence of Hilbert Cusp Forms with Non-vanishing L-values
Canadian journal of mathematics, Tome 68 (2016) no. 4, pp. 908-960

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DOI

We develop a derivative version of the relative trace formula on $\text{PGL}\left( 2 \right)$ studied in our previous work, and derive an asymptotic formula of an average of central values (derivatives) of automorphic $L$ -functions for Hilbert cusp forms. As an application, we prove the existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are arbitrarily large.
DOI : 10.4153/CJM-2015-048-4
Mots-clés : 11F67, 11F72, automorphic representations, relative trace formulas, central L–values, derivatives of L–functions 
Sugiyama, Shingo; Tsuzuki, Masao. Existence of Hilbert Cusp Forms with Non-vanishing L-values. Canadian journal of mathematics, Tome 68 (2016) no. 4, pp. 908-960. doi: 10.4153/CJM-2015-048-4
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     title = {Existence of {Hilbert} {Cusp} {Forms} with {Non-vanishing} {L-values}},
     journal = {Canadian journal of mathematics},
     pages = {908--960},
     year = {2016},
     volume = {68},
     number = {4},
     doi = {10.4153/CJM-2015-048-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-048-4/}
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