TY  - BOOK
AU  - Cao, Liping 
AU  - Lin, Bernard L. S. 
TI  - Proofs of some conjectures of Sun on the relations between t(a, b, c; n) and N(a, b, c; n) (Journal Article)
SN  - 0019-5588
PY  - 2023///
CY  - New Delhi
PB  - :Indian National Science Academy | Springer
KW  - Ramanujan’s theta function identities| Sum of squares| Sum of triangular numbers
N1  - ***______{For Hard Copy, Please visit Library.}________***



N2  - 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
UR  - https://doi.org/10.1007/s13226-022-00324-8
ER  -