On a product of three theta functions and the number of representations of integers as mixed ternary sums involving squares, triangular, pentagonal and octagonal numbers

2024/10/17 by Nasser Abdo Saeed Bulkhali, Bulkhali, N. A. S., Gedela Kavya Keerthana +3
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2410.13555

Abstract

In this paper, we derive a general formula to express the product of three theta functions as a linear combination of other products of three theta functions. Moreover, we use the main formula to deduce a general formula for the product of two theta functions. Furthermore, as applications, we extract several theorems in the theory of representation of integers as mixed ternary sums involving squares, triangular numbers, generalized pentagonal numbers and generalized octagonal numbers

Related

• Ramanujan's theta functions and linear combinations of three triangular numbers
• Ramanujan's theta functions and sums of triangular numbers
• Integer Matrix Exact Covering Systems and Product Identities for Theta Functions
• The number of representations by a ternary sum of triangular numbers
• Ternary Sums of Squares and Triangular Numbers