广义立方分区和以质数为模数的过分区的算术性质

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-09-10 DOI:10.1007/s00010-024-01116-7

Tewodros Amdeberhan, James A. Sellers, Ajit Singh

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引用次数: 0

摘要

立方分割是一种整数分割，其中偶数部分可以出现两种颜色。在本文中，我们引入了广义立方分割的概念，并证明了许多类似于经典拉曼努强类型的新同余式。我们强调两种证明方法，一种是基本方法（主要依赖于函数方程），另一种是基于模块形式的方法。最后，我们证明了广义超立方分区的类似结果。

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Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime

A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.