Note on \(p\)-adic Hermitian Eisenstein series
type: Item
instance of: scholarly article
title: Note on \(p\)-adic Hermitian Eisenstein series
zbMATH Open document ID: 1132.11022
DOI: 10.1007/BF02960867
author: T. Munemoto
author: Shoyu Nagaoka
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2007-08-29T00:00:00Z
review text: In a series of papers, the second author of this article has investigated the arithmetic properties of Serre's \(p\)-adic Eisenstein series and its variants concerning Siegel and Hermitian modular forms. He found a curious formula which shows the coincidence between a \(p\)-adic Siegel Eisenstein series and a genus theta series. In [Proc. Am. Math. Soc. 134, No. 9, 2533--2540 (2006; Zbl 1157.11017)] he announced that such a phenomenon also occurs in the case of Hermitian modular forms for \(\mathbb{Q}(i)\). In the present article, this result is extended to the case of Hermitian modular forms attached to any imaginary quadratic field with class number one (Theorem 3.1).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 5184540
zbMATH Keywords: \(p\)-adic modular form
zbMATH Keywords: Eisenstein series
zbMATH Keywords: Siegel Eisenstein series
zbMATH Keywords: Hermitian modular form
zbMATH Keywords: genus theta series
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5184540