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三组l-正则分拆函数的同余性质

于敬军

高师理科学刊2025，Vol.45Issue(6)：27-30,4.

高师理科学刊2025，Vol.45Issue(6)：27-30,4.DOI:10.3969/j.issn.1007-9831.2025.06.006

三组l-正则分拆函数的同余性质

Congruence properties for three l-regular partition functions

于敬军¹

作者信息

1. 杭州科技职业技术学院基础教学部,浙江杭州 311402
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摘要

Abstract

Let bl(n)denote the l-regular partitions of positive integer n.By using q-series and the theory of Hecke operator theory in modular form,two congruence relations for b7(n)and b23(n)modulo 2 are proven,namely,for i∈{3,4,6},the congruence relations b7(14n+2i+1)≡0(mod 2)holds,furthermore,for j∈{7,10,14,15,18,19,20,21,22},the congruence relations b23(46n+2j+1)≡0(mod 2)holds.Meanwhile,by using a congruence equation discovered by Baruah and Berndt and combining with a q-series identity,the congruence relation b25(10n+4)≡2b25(5n-1)+b25(20n+4)(mod 25)is proved.

关键词

分拆函数/正则分拆/同余/Hecke算子

Key words

partition function/regular partition/congruence/Hecke operator

分类

数理科学

引用本文复制引用

于敬军..三组l-正则分拆函数的同余性质[J].高师理科学刊,2025,45(6):27-30,4.

高师理科学刊

ISSN：1007-9831

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