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Some congruence properties for -regular partitions, where l ∈ {4, 8, 13, 17, 19, 25, 40, 55}

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Some congruence properties for -regular partitions, where l ∈ {4, 8, 13, 17, 19, 25, 40, 55}

Abstract

Some congruence properties for -regular partitions, where l ∈ {4, 8, 13, 17, 19, 25, 40, 55}

참고문헌 (21)

  1. Abinash, S, "Some New Congruences for ℓ-Regular Partitions Modulo 13, 17, and 23", Hardy-Ramanujan Journal, Hardy-Ramanujan So-ciety, 42 (2020)
  2. Adiga, C., "Congruences for 7 and 49-regular partitions modulo powers of 7", Ramanujan J, 46, pp.821~833 (2018)
  3. Baruah, N.D., "Generating functions and congruences for 9-regular and 27-regular partitions in 3 colours", Hardy-Ramanujan J, 44, pp.102~115 (2021)
  4. Berndt, B.C., "Ramanujan's Notebooks. Part III" (1991), Springer
  5. Berndt, B.C., "Ramanujan's Notebooks. Part IV" (1994), Springer
  6. Berndt, B. C., "Theorems on partition from a page in Ramanujan's lost notebook", J. Comput. Appl. Math, 160, pp.53~68 (2003)
  7. Berndt, B.C., "Number Theory in the Spirit of Ramanujan" (2006), Amer. Math. Soc
  8. Boll, E., "The 7-regular and 13-regular partition functions modulo 3", Bulletin of the Austr. Math. Soc, 93(3), pp.410~419 (2016)
  9. Calkin, N., "Divisibility properties of the 5-regular and 13-regular partition functions", Integers, 8(1) (2008)
  10. Carlson, R., "Innite families of congruences for k-regular partitions", Ramanujan J, 33, pp.329~337 (2014)
  11. Chern, S., "Arithmetic properties for 7-regular partition triples", Indian J. Pure Appl. Math, 51, pp.717~733 (2020)
  12. Cui, S. P., "Arithmetic properties of ℓ-regular partitions", Adv. in Appl. Math, 51, pp.507~523 (2013)
  13. Dai, H. B., "On the distribution of odd values of 2a-regular partition functions", J. Number Theory, 143, pp.14~23 (2013)
  14. Furcy, D., "Congruences for ℓ-regular partition functions modulo 3", Ramanujan J, 27, pp.101~108 (2012)
  15. Hirschhorn, M.D., "Analytic number theory, modular forms and q-hypergeometric series", pp.311~328 (2017)
  16. Hou, Q. -H., "Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7", Adv. Appl. Math, 70, pp.32~44 (2015)
  17. Ramanujan S., "Collected Papers" (1962), chelsea
  18. Ranganatha, D., "Ramanujan-type congruences modulo powers of 5 and 7", Indian J. Pure Appl. Math, 48(3), pp.449~465 (2017)
  19. Watson, G.N., "Theorems Stated by Ramanujan (VII): Theorems on Continued Frac-tions", J. London Math. Soc, s1-4, pp.39~48 (1929)
  20. Webb, J.J., "Arithmetic of the 13-regular partition function modulo 3", Ramanujan J, 25, pp.49~56 (2011)
  21. Xia, E.X.W., "Congruences for some ℓ-regular partitions modulo ℓ", J. Number Theory, 152, pp.105~117 (2015)

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