A Study on the Number of Representations of an Integer into Certain Quadratic Forms

2024/01/15 by Kritika Kashyap, Kashyap, Kritika
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.07811

openalex publication_date 2024/01/15 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

Abstract

Let a_k(n) denotes the number of representations of a non-negative integer n as sum of k quadratic forms of the type x²+xy+y² and a_{λ1,λ2,λ3…λk}(n) denotes the number of representations n as a linear combination of k quadratic forms of the aforementioned type, where λ_i's are positive integers. The expressions for a_k(n) and a_{λ1,λ2,λ3…λk}(n) for different values of k and λ_i are available in the literature. In this project, we attempt to find relationships among some of these particular a_{λ1,λ2,λ3…λk}(n)'s in a generalized manner.

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