Modular forms on the Fricke group
type: Item
instance of: scholarly article
title: Modular forms on the Fricke group
zbMATH Open document ID: 0851.11027
DOI: 10.1007/BF02953336
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1996-06-19T00:00:00Z
review text: Sei \(p\) eine feste Primzahl und \(\Gamma_0 (p) = \Bigl\{ (\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}) \in SL(2,\mathbb{Z}) \mid c \equiv 0 \bmod p \Bigr\}\). Die zu \(\Gamma_0 (p)\) gehörende Fricke-Gruppe \(\Gamma_* (p)\) ist gegeben durch die Zerlegung \(\Gamma_* (p) = \Gamma_0 (p) \cup \Gamma_0 (p)W_p\) mit \(W_p = (\begin{smallmatrix} 0 & - {1 \over \sqrt p} \\ \sqrt p & 0 \end{smallmatrix})\). Hier wird, in Abhängigkeit von \(\Gamma_0 (p)\), der Raum der automorphen Formen vom Gewicht \(k \in \mathbb{N}\) detailliert beschrieben. Als Anwendung ergeben sich schöne Identitäten für die zu \(p\)-modularen Gittern gehörenden Theta-Reihen.
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 878387
zbMATH Keywords: modular forms
zbMATH Keywords: Fricke groups
zbMATH Keywords: space of automorphic forms
zbMATH Keywords: theta series
zbMATH Keywords: \(p\)-modular lattices
author: Aloys Krieg
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878387