Congruences modulo 4 for the number of 3-regular partitions

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI:10.5802/crmath.512

Cristina Ballantine, Mircea Merca

引用次数: 0

Abstract

The last decade has seen an abundance of congruences for b ℓ (n), the number of ℓ-regular partitions of n. Notably absent are congruences modulo 4 for b 3 (n). In this paper, we introduce Ramanujan type congruences modulo 4 for b 3 (2n) involving some primes p congruent to 11,13,17,19,23 modulo 24.

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对3正则分区数取模4的同余

在过去的十年中，我们已经看到了大量的对b_3 (n)的同余，n的n -正则分割的数量。值得注意的是，缺少对b_3 (n)模4的同余。在本文中，我们引入了对b_3 (n)模4的Ramanujan型同余，涉及一些素数p同于11、13、17、19、23模24。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.