Skip to content
DraconiticResearch
Search Sources API
186,631 studies31 sourcesUpdated 54 min ago
PreprintCC BY 4.0arXiv

An elementary approach to Sun Kim's general theta function identities

  • Dazhao Tang
Open at sourcePDFDOICite

Abstract

Ramanujan's modular equations of degrees $3$, $5$, $7$, $11$ and $23$ are closely related to certain theta function identities. Warnaar generalized the identities arising from the modular equations of degrees $3$ and $7$ to a general theta function identity. Kim subsequently obtained a further general theta function identity associated with the modular equations of degrees $5$, $11$ and $23$, and established several general theta function identities containing known partition theorems as special cases. In this paper, we present an elementary approach to Kim's general theta function identities, yielding q-series proofs of these identities within a common framework.

Related

  1. Parameterized partial theta identities and a unified q-difference proof
    Chen-Yang Su
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Siegel-Weil type identities for general linear groups related to parabolic induction from two Speh representations
    David Ginzburg, David Soudry
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Computing Theta Characteristics and their Galois action on general curves of moderate genus
    Thibaut Misme
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. The Riemann theta function near soliton limit
    Yuji Kodama
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  5. Dyadic Structure of the Two-Block Odd Partition Function and Theta-Weighted Congruences for pod(n)
    Mircea Merca
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{tang2026elementary,
  title = {{An elementary approach to Sun Kim's general theta function identities}},
  author = {Dazhao Tang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09751},
  eprint = {2609.09751},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09751},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An elementary approach to Sun Kim's general theta function identities
AU  - Dazhao Tang
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09751
UR  - https://arxiv.org/abs/2609.09751
AB  - Ramanujan's modular equations of degrees $3$, $5$, $7$, $11$ and $23$ are closely related to certain theta function identities. Warnaar generalized the identities arising from the modular equations of degrees $3$ and $7$ to a general theta function identity. Kim subsequently obtained a further general theta function identity associated with the modular equations of degrees $5$, $11$ and $23$, and established several general theta function identities containing known partition theorems as special cases. In this paper, we present an elementary approach to Kim's general theta function identities, yielding q-series proofs of these identities within a common framework.
ER  -