본문 바로가기
KERD
논문KCI 등재

A NEW q-ANALOGUE OF VAN HAMME’S (G.2) SUPERCONGRUENCE FOR PRIMES p ≡ 3 (mod 4)

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

Van Hamme's (G.2) supercongruence modulo $p^4$ for primes $p\equiv 3 \pmod 4$ and $p>3$ was first established by Swisher. A $q$-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new $q$-analogue of Van Hamme's (G.2) supercongruence for $p\equiv 3\pmod{4}$.

Abstract

Van Hamme's (G.2) supercongruence modulo $p^4$ for primes $p\equiv 3 \pmod 4$ and $p>3$ was first established by Swisher. A $q$-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new $q$-analogue of Van Hamme's (G.2) supercongruence for $p\equiv 3\pmod{4}$.

참고문헌 (22)

  1. Mohamed El Bachraoui, "On supercongruences for truncated sums of squares of basic hypergeometric series", The Ramanujan Journal, 54(2), pp.415~426 (2020), Springer Science and Business Media LLC[DOI]
  2. B. C. Berndt, "Ramanujan, History of Mathematics", pp.9~ (1995), American Mathematical Society
  3. G. Gasper, "Encyclopedia of Mathematics and its Applications", pp.96~ (2004), Cambridge University Press
  4. Victor J. W. Guo, "A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial", Israel Journal of Mathematics, 240(2), pp.821~835 (2020), Springer Science and Business Media LLC[DOI]
  5. V. J. W. Guo, "A new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial", Results Math, 75(155), pp.13~ (2020)
  6. Victor J. W. Guo, "Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series", Constructive Approximation, 53(1), pp.155~200 (2020), Springer Science and Business Media LLC[DOI]
  7. Victor J.W. Guo, "A q-microscope for supercongruences", Advances in Mathematics, 346, pp.329~358 (2019), Elsevier BV[DOI]
  8. V. J. W. Guo, "Dwork-type supercongruences through a creative q-microscope", J. Combin. Theory, Ser. A, 178(105362), pp.37~ (2021)
  9. L. van Hamme, "Some conjectures concerning partial sums of generalized hypergeometric series, in p-adic functional analysis (Nijmegen, 1996)", Lecture Notes in Pure and Appl. Math, 192, pp.223~236 (1997), Dekker
  10. G. H. Hardy, "A chapter from Ramanujan's note-book", Proc. Cambridge Philos. Soc, 21(2), pp.492~503 (1923)
  11. Bing He, "Supercongruences on Truncated Hypergeometric Series", Results in Mathematics, 72(1-2), pp.303~317 (2016), Springer Science and Business Media LLC[DOI]
  12. Ji-Cai Liu, "On a congruence involving q-Catalan numbers", Comptes Rendus. Mathématique, 358(2), pp.211~215 (2020), Cellule MathDoc[DOI]
  13. JI-CAI LIU, "A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES", Bulletin of the Australian Mathematical Society, 102(3), pp.353~359 (2020), Cambridge University Press (CUP)[DOI]
  14. Ji-Cai Liu, "On the divisibility of sums of even powers of q-binomial coefficients", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 116(2) (2022), Springer Science and Business Media LLC[DOI]
  15. Yudong Liu, "q-analogues of the (G.2) supercongruence of Van Hamme", Rocky Mountain Journal of Mathematics, 51(4) (2021), Rocky Mountain Mathematics Consortium[DOI]
  16. Y. Liu, "Some q-supercongruences from a quadratic transformation by Rahman", Results Math, 77(44), pp.14~ (2022)
  17. Yudong Liu, "Further q-analogues of the (G.2) supercongruence of Van Hamme", The Ramanujan Journal, 59(3), pp.791~802 (2022), Springer Science and Business Media LLC[DOI]
  18. Ling Long, "Some supercongruences occurring in truncated hypergeometric series", Advances in Mathematics, 290, pp.773~808 (2016), Elsevier BV[DOI]
  19. Y. Morita, "A p-adic analogue of the Γ-function", J. Fac. Sci. Univ. Tokyo Sect. IA Math, 22(2), pp.255~266 (1975)
  20. Holly Swisher, "On the supercongruence conjectures of van Hamme", Research in the Mathematical Sciences, 2(1) (2015), Springer Science and Business Media LLC[DOI]
  21. Chuanan Wei, "Some q-supercongruences modulo the fourth power of a cyclotomic polynomial", Journal of Combinatorial Theory, Series A, 182, pp.105469~ (2021), Elsevier BV[DOI]
  22. Chang Xu, "Proofs of Guo and Schlosser’s two conjectures", Periodica Mathematica Hungarica, 85(2), pp.474~480 (2022), Springer Science and Business Media LLC[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (18건)