Non-vanishing of Rankin-Selberg convolutions for Hilbert modular forms

被引:0
作者
Alia Hamieh
Naomi Tanabe
机构
[1] University of Northern British Columbia,Department of Mathematics and Statistics
[2] Bowdoin College,Department of Mathematics
来源
Mathematische Zeitschrift | 2021年 / 297卷
关键词
Hilbert modular forms; Rankin-Selberg ; -functions; Non-vanishing of central ; -values; Primary 11F41; 11F67; Secondary 11F30; 11F11; 11F12; 11N75;
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摘要
In this paper, we study the non-vanishing of the central values of the Rankin-Selberg L-function of two adelic Hilbert primitive forms f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{f}$$\end{document} and g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{g}$$\end{document}, both of which have varying weight parameter k. We prove that, for sufficiently large k∈2Nn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\in 2{\mathbb {N}}^n$$\end{document}, there are at least N(k)logcN(k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\mathrm{N}(k)}{\log ^c \mathrm{N}(k)}$$\end{document} adelic Hilbert primitive forms f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{f}$$\end{document} of weight k for which L(12,f⊗g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(\frac{1}{2}, \mathbf{f}\otimes \mathbf{g})$$\end{document} are nonzero.
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页码:81 / 97
页数:16
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