Anticyclotomic p-adic L-functions and Ichino’s formula
Anticyclotomic p-adic L-functions and Ichino’s formula
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反环剖 p 进 L 函数和 Ichino 公式
DOI：
10.1007/s40316-019-00118-1
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Dan J. Collins
中科院分区：
文献类型：
--
作者：
Dan J. Collins
We give a new construction of a p-adic L-function L(f,Ξ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {L}}(f,\Xi )$$\end{document}, for f a holomorphic newform and Ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Xi $$\end{document} an anticyclotomic family of Hecke characters of Q(-d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Q}(\sqrt{-d})$$\end{document}. The construction uses Ichino’s triple product formula to express the central values of L(f,ξ,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(f,\xi ,s)$$\end{document} in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what happens when f is replaced by a modular form congruent to it modulo p, and has future applications in the case where f is residually reducible.
We give a new construction of a p-adic L-function L(f,Ξ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {L}}(f,\Xi )$$\end{document}, for f a holomorphic newform and Ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Xi $$\end{document} an anticyclotomic family of Hecke characters of Q(-d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Q}(\sqrt{-d})$$\end{document}. The construction uses Ichino’s triple product formula to express the central values of L(f,ξ,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(f,\xi ,s)$$\end{document} in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what happens when f is replaced by a modular form congruent to it modulo p, and has future applications in the case where f is residually reducible.
岩泽理论的精炼
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
坂井聡;宮崎英一;Masato Kurihara
通讯作者：
Masato Kurihara
扭曲三重积 L 函数的异常零点
DOI：
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发表时间：
2021
期刊：
影响因子：
--
作者：
L. Demonet;O. Iyama;N. Reading;I. Reiten;H. Thomas;Shunsuke Yamana
通讯作者：
Shunsuke Yamana
DOI：
--
发表时间：
1984
期刊：
--
影响因子：
--
作者：
M. Wodzicki
通讯作者：
M. Wodzicki