01339nam a22002057a 4500 20240205120809.0 240205b ||||| |||| 00| 0 eng d 0019-5588 Cao, Liping Proofs of some conjectures of Sun on the relations between t(a, b, c; n) and N(a, b, c; n) (Journal Article) New Delhi :Indian National Science Academy | Springer ,2023 1081-1098p. Indian Journal of Pure and Applied Mathematics , Volume 54: Number 4, December 2023 ***______{For Hard Copy, Please visit Library.}________*** Abstract: Let and be the set of integers and the set of positive integers, respectively. For and, let N(a, b, c; n) be the number of representations of n as and t(a, b, c; n) be the number of representations of n as.Recently, Sun established many relations between t(a, b, c; n) and and listed 43 relations need to be confirmed. More recently, Xia and Zhang proved 19 relations conjectured by Sun. In this paper, by employing Ramanujan’s theta function identities, we prove the remaining 24 relations. Ramanujan’s theta function identities| Sum of squares| Sum of triangular numbers Lin, Bernard L. S. https://doi.org/10.1007/s13226-022-00324-8 PER 0 0 0 0 RIEBPL RIEBPL 2024-02-05 0 2024-02-05 00:00:00 2024-02-05 PER 45413 45412