Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7
Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these g...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hou, Qing-Hu [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Umfang: |
13 |
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| Übergeordnetes Werk: |
Enthalten in: Kiiacylphnols A−H, eight undescribed polycyclic polyprenylated acylphloroglucinols with anticancer activities from - Duan, Yulin ELSEVIER, 2022, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:70 ; year:2015 ; pages:32-44 ; extent:13 |
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10.1016/j.aam.2015.06.005 |
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| 520 | |a Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. | ||
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10.1016/j.aam.2015.06.005 doi GBVA2015007000028.pica (DE-627)ELV018360599 (ELSEVIER)S0196-8858(15)00070-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 580 540 VZ BIODIV DE-30 fid 42.00 bkl Hou, Qing-Hu verfasserin aut Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7 2015 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. 11P83 Elsevier 05A17 Elsevier Sun, Lisa H. oth Zhang, Li oth Enthalten in Elsevier Duan, Yulin ELSEVIER Kiiacylphnols A−H, eight undescribed polycyclic polyprenylated acylphloroglucinols with anticancer activities from 2022 Amsterdam [u.a.] (DE-627)ELV007875029 volume:70 year:2015 pages:32-44 extent:13 https://doi.org/10.1016/j.aam.2015.06.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 42.00 Biologie: Allgemeines VZ AR 70 2015 32-44 13 045F 510 |
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10.1016/j.aam.2015.06.005 doi GBVA2015007000028.pica (DE-627)ELV018360599 (ELSEVIER)S0196-8858(15)00070-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 580 540 VZ BIODIV DE-30 fid 42.00 bkl Hou, Qing-Hu verfasserin aut Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7 2015 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. 11P83 Elsevier 05A17 Elsevier Sun, Lisa H. oth Zhang, Li oth Enthalten in Elsevier Duan, Yulin ELSEVIER Kiiacylphnols A−H, eight undescribed polycyclic polyprenylated acylphloroglucinols with anticancer activities from 2022 Amsterdam [u.a.] (DE-627)ELV007875029 volume:70 year:2015 pages:32-44 extent:13 https://doi.org/10.1016/j.aam.2015.06.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 42.00 Biologie: Allgemeines VZ AR 70 2015 32-44 13 045F 510 |
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Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7 |
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Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. |
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Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. |
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Let b ℓ ( n ) be the number of ℓ-regular partitions of n. We show that the generating functions of b ℓ ( n ) with ℓ = 3 , 5 , 6 , 7 and 10 are congruent to the products of two items of Ramanujan's theta functions ψ ( q ) , f ( − q ) and ( q ; q ) ∞ 3 modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for b ℓ ( n ) modulo 3, 5 and 7. |
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