논문KCI 등재
5 REGULAR PARTITIONS WITH DISTINCT ODD PARTS
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In this article, we prove infinite families of congruences for pod5(n) (the number of 5-regular partitions of n with distinct odd parts (and even parts are unrestricted)) using the theory of Hecke eigenforms. We also study the divisibility properties of pod5(n) using the arithmetic properties of modular forms.
Abstract
In this article, we prove infinite families of congruences for pod5(n) (the number of 5-regular partitions of n with distinct odd parts (and even parts are unrestricted)) using the theory of Hecke eigenforms. We also study the divisibility properties of pod5(n) using the arithmetic properties of modular forms.
참고문헌 (11)
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- B. Gordon, "Divisibility of certain partition functions by powers of primes", Ramanujan J, 1, pp.25~34 (1997)
- M. D. Hirschhorn, "The Power of q, Developments in Mathematics 49" (2017), Springer
- M. D. Hirschhorn, "Arithmetic properties of partitions with odd parts distinct", Ramanujan J, 22, pp.273~284 (2010)
- M. D. Hirschhorn, "Elementary proofs of parity results for 5-regular partitions", Bull. Aust. Math. Soc, 81, pp.58~63 (2010)
- Y. Martin, "Multiplicative eta-quotients", T. Am. Math. Soc, 348, pp.4825~4856 (1996)
- K. Ono, "The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series:Arithmetic of the Coefficients of Modular Forms and Q-series" (2004), American Mathematical Soc
- S. Radu, "Congruence properties modulo 5 and 7 for the pod function", Int. J. Number Theory, 7, pp.2249~2259 (2011)
- C. Ray, "On Andrews’ integer partitions with even parts below odd parts", J. Number Theory, 215, pp.321~338 (2020)
- E. X. W. Xia, "Analogues of Ramanujans partition identities", Ramanujan J, 31, pp.373~396 (2013)
관련 논문AI추천
On 5-regular bipartitions with odd parts distinctHARISHKUMAR T., M. S. MAHADEVA NAIKA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제2호ON (2,5)-REGULAR BIPARTITIONS WITH ODD PARTS DISTINCTM. Prasad장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호ARITHMETIC PROPERTIES OF PARTITIONS WITH 5-CORESB. HEMANTHKUMAR, H. S. SUMANTH BHARADWAJ, M. S. MAHADEVA NAIKA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호New congruences for $\ell$-regular overpartitionsAnkita Jindal, Nabin K. Meher대한수학회 · 대한수학회지2022 · 제59권 제5호Congruences modulo 7 and 11 for (s,t)-regular bipartitionsRanganatha D.장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호Some Congruence Properties for Ramanujan’s General PartitionsB. R. S. Kumar, D. A. Radha, Shruthi Hegde장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호
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