The number of representations of integers by 4-dimensional strongly \(N\)-modular lattices
type: Item
instance of: scholarly article
title: The number of representations of integers by 4-dimensional strongly \(N\)-modular lattices
zbMATH Open document ID: 1491.11038
author: H. Y. Jung
author: Chang Heon Kim
author: Kyoungmin Kim
author: Soonhak Kwon
published in: The Ramanujan Journal
publication date: 2022-03-21T00:00:00Z
review text: In this work, the authors proved that a space of cusp forms of weight \(2\) with level \(N\)and real character \(\chi \) has dimension \(1\) if and only if \(\chi \) is trivial and \[ N\in\{11,14,15,17,19,20,21,24,27,32,36,49\} \] and derive bases for spaces of cusp forms of weight \(2\) with trivial character and \[ N\in \{17,19,21,49\}. \] Further they provided formulas for the number of representations of integers by \(4\)-dimensional strongly \(N\)-modular lattices for \[ N\in \{11,14,15,17,19,20,21,24,27,32,36\}. \]
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11E45
zbMATH DE Number: 7493916
zbMATH Keywords: spaces of cusp forms
zbMATH Keywords: eta-quotients
zbMATH Keywords: Hecke operators
zbMATH Keywords: strongly \(N\)-modular lattices
zbMATH Keywords: Minkowski-Siegel formula
reviewed by: Ahmet Tekcan
MaRDI profile type: Publication
full work available at URL: s11139-021-00490-z
OpenAlex ID: W3200849359
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DOI: 10.1007/S11139-021-00490-Z
description: scientific article; zbMATH DE number 7493916