An Identity of Ramanujan and the Representation of Integers as Sums of Triangular Numbers

@article{Liu2003AnIO,
  title={An Identity of Ramanujan and the Representation of Integers as Sums of Triangular Numbers},
  author={Zhi-Guo Liu},
  journal={The Ramanujan Journal},
  year={2003},
  volume={7},
  pages={407-434}
}
  • Zhi-Guo Liu
  • Published 1 December 2003
  • Mathematics
  • The Ramanujan Journal
Let k be a positive number and tk(n) denote the number of representations of n as a sum of k triangular numbers. In this paper, we will calculate t2k(n) in the spirit of Ramanujan. We first use the complex theory of elliptic functions to prove a theta function identity. Then from this identity we derive two Lambert series identities, one of them is a well-known identity of Ramanujan. Using a variant form of Ramanujan's identity, we study two classes of Lambert series and derive some theta… Expand
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