Parity of the 8-regular partition function

被引：1

作者：

Cherubini, Giacomo ^{[1
,2
]}

Mercuri, Pietro ^{[3
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 8, Czech Republic

[2] Sapienza Univ Roma, Ist Nazl Alta Matemat Francesco Severi, Dipartimento Matemat Guido Castelnuovo, Res Unit, Piazzale Aldo Moro 5, I-00135 Rome, Italy

[3] Sapienza Univ Roma, Dipartimento Sbai, Via A Scarpa 10, I-00161 Rome, Italy

来源：

RAMANUJAN JOURNAL | 2024年 / 63卷 / 03期

关键词：

Congruences; Regular partitions; Dedekind eta-function; Modular forms;

D O I：

10.1007/s11139-023-00784-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a complete characterisation of the parity of b(8)(n), the number of 8-regular partitions of n. Namely, we prove that b(8)(n) is odd precisely when 2(4a+7 )has the form p4(a+1)m(2) with p prime and p <does not divide> m.

引用

页码：715 / 722

页数：8

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