Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 12 min ago
PreprintarXiv licencearXiv

q-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial

  • Liton Karmakar
  • Arijit Jana
Open at sourcePDFDOICite

Abstract

In this paper, we establish several q-supercongruences for basic hypergeometric series modulo the third and fifth powers of a cyclotomic polynomial. These results extend several existing supercongruences related to the (A.2) and (C.2) supercongruences of Van Hamme. Our proofs employ the creative microscoping method developed by Guo and Zudilin \cite{guo2019q}, together with Watson's 8ϕ7 transformation formula.

Related

  1. Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta-functions
    Dandan Chen, Rong Chen, Frank G. Garvan
    The Ramanujan JournalPeer-reviewedLicence not statedFull text5 citedAlgebra & number theoryOpenAlex
  2. Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts
    Manjil P. Saikia, Prabal Talukdar, Dazhao Tang
    arXivPreprintCC0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Congruences modulo powers of $7$ for partitions with colored odd parts
    Saikat Maity, Manjil P. Saikia, Prabal Talukdar
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Fixed points and exact periods of Chebyshev polynomials modulo odd prime powers
    Chatchawan Panraksa, Aram Tangboonduangjit
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryDynamical systemsarXiv
  5. Generalized Frobenius Partitions Modulo Powers of $2$
    Manjil P. Saikia
    arXivPreprintCC0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{karmakar2026qsupercongruences,
  title = {{$q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial}},
  author = {Liton Karmakar and Arijit Jana},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11778},
  eprint = {2610.11778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11778},
}
RIS
TY  - UNPB
TI  - q-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial
AU  - Liton Karmakar
AU  - Arijit Jana
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11778
UR  - https://arxiv.org/abs/2610.11778
AB  - In this paper, we establish several q-supercongruences for basic hypergeometric series modulo the third and fifth powers of a cyclotomic polynomial. These results extend several existing supercongruences related to the (A.2) and (C.2) supercongruences of Van Hamme. Our proofs employ the creative microscoping method developed by Guo and Zudilin \cite{guo2019q}, together with Watson's _8ϕ_7 transformation formula.
ER  -