Affiliation:
1. Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China
Abstract
In a recent paper, Sun posed six conjectures on the relations between [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the number of representations of [Formula: see text] as [Formula: see text], where [Formula: see text] are positive integers, [Formula: see text] are arbitrary nonnegative integers, and [Formula: see text] denotes the number of representations of [Formula: see text] as [Formula: see text], where this time [Formula: see text] are integers. In this paper, we prove Sun’s six conjectures by using Ramanujan’s theta function identities.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
10 articles.
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1. Proofs of some conjectures of Sun on the relations between t(a, b, c; n) and N(a, b, c; n);Indian Journal of Pure and Applied Mathematics;2022-08-31
2. Proofs of some conjectures of Sun on the relations between T(a,b,c,d;n) and N(a,b,c,d;n);Rocky Mountain Journal of Mathematics;2022-06-01
3. Automatic proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers;The Ramanujan Journal;2022-05-14
4. On Conjectures of Z.-H. Sun;Results in Mathematics;2022-04-01
5. Proofs of some conjectures on the reciprocals of the Ramanujan–Gordon identities;The Ramanujan Journal;2020-07-16