Jacobi's cubic analog of the pentagonal number theorem and representations of 24n+5 as a sum of two squares

被引：0

作者：

Ballantine, Cristina ^{[1
]}

Merca, Mircea ^{[2
,3
]}

机构：

[1] Coll Holy Cross, Dept Math & Comp Sci, Worcester, MA 01610 USA

[2] Natl Univ Sci & Technol Politehn Bucharest, Fundamental Sci Appl Engn Res Ctr, Dept Math Methods & Models, Bucharest 060042, Romania

[3] Acad Romanian Scientists, Bucharest 060042, Romania

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2025年 / 119卷 / 02期

关键词：

Partitions; Theta series; Pentagonal number theorem; Ramanujan type congruences; SIMPLE PROOF;

D O I：

10.1007/s13398-025-01702-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the two squares problem in order to introduce a combinatorial interpretation for Jacobi's cubic analog of Euler's pentagonal number theorem. Under certain conditions imposed by Fermat's theorem on representations of integers as a sum of two squares, we derive a linear homogeneous recurrence relation for Euler's partition function. In this context, we introduce two infinite conjectural families of Ramanujan type congruences and prove several special cases.

引用

页数：13

共 1 条

[1] Jacobi’s cubic analog of the pentagonal number theorem and representations of 24n+5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$24n+5$$\end{document} as a sum of two squaresJacobi’s cubic analog of the pentagonal number theorem...C. Ballantine et al.
Cristina Ballantine
Mircea Merca
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2025, 119 (2):

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