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In this note we give a detailed construction of a Λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda $$\end{document}-adic d\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathfrak d$$\end{document}th Shintani lifting. We obtain a Λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda $$\end{document}-adic version of Kohnen’s formula relating Fourier coefficients of half-integral weight modular forms and special values of twisted L-series. As a by-product, we derive a mild generalization of such classical formulae, and also point out a relation between Fourier coefficients of Λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Lambda $$\end{document}-adic d\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathfrak d$$\end{document}th Shintani liftings and Stark–Heegner points.
Annales mathématiques du Québec – Springer Journals
Published: Oct 1, 2022
Keywords: Shintani lifting; Modular forms of half-integral weight; Hida families; L-values of modular forms; 11F33; 11F27; 11F37
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