The number of representations of integers by 4-dimensional strongly N-modular lattices

被引：0
|
作者：
Jung, Ho Yun [1 ]
Kim, Chang Heon [2 ]
Kim, Kyoungmin [2 ,3 ]
Kwon, Soonhak [2 ]
机构：
[1] Dankook Univ, Dept Math, Cheonan 31116, South Korea
[2] Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea
[3] Hannam Univ, Dept Math, Daejeon 34430, South Korea
来源：
RAMANUJAN JOURNAL | 2022年 / 57卷 / 04期
基金：
新加坡国家研究基金会;
关键词：
Spaces of cusp forms; Eta-quotients; Hecke operators; Strongly N-modular lattices; The Minkowski-Siegel formula;
D O I：
10.1007/s11139-021-00490-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we prove 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 is 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 is an element of {17, 19, 21, 49}. As applications, we provide 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}.
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页码：1253 / 1275
页数：23
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