https://scholars.lib.ntu.edu.tw/handle/123456789/638960
標題: | Four-variable p-adic triple product L-functions and the trivial zero conjecture | 作者: | MING-LUN HSIEH Yamana, Shunsuke |
公開日期: | 1-一月-2023 | 來源出版物: | Mathematische Annalen | 摘要: | We construct the four-variable primitive p-adic L-functions associated with the triple product of Hida families and prove the explicit interpolation formulae at all critical points in the balanced range. Our construction is to carry out the p-adic interpolation of Garrett’s integral representation of triple product L-functions via the p-adic Rankin-Selberg convolution method. The main novelty in this paper is the construction and the patching of four p-adic families of the pull-back of nearly holomorphic Siegel Eisenstein series on GSp (6) . As an application, we obtain the cyclotomic p-adic L-function for the motive associated with the triple product of p-ordinary elliptic curves and prove the trivial zero conjecture for this motive. In particular, this proves the first cases of the Greenberg-Benois trivial zero conjecture where multiple trivial zeros are present and the Galois representation is not of GL (2) -type. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/638960 | ISSN: | 00255831 | DOI: | 10.1007/s00208-023-02768-7 |
顯示於: | 數學系 |
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