A new identity for (q; q)∞10 with an application to Ramanujan's partition congruence modulo 11

Bruce C. Berndt; Song Heng Chan; Zhi Guo Liu; Hamza Yesilyurt

doi:10.1093/qmath/hag038

A new identity for (q; q)_∞¹⁰ with an application to Ramanujan's partition congruence modulo 11

Bruce C. Berndt^*
, Song Heng Chan
, Zhi Guo Liu
, Hamza Yesilyurt

^*此作品的通讯作者

数学科学学院

University of Illinois Urbana–Champaign

科研成果: 期刊稿件 › 文章 › 同行评审

27 引用（Scopus）

摘要

A new identity for the tenth power of the Dedekind eta-funtion η(z) is established. This is used to give a short proof of Ramanujan's congruence p(11n + 6) ≡ 0 (mod 11) and to prove the lacunarity of η¹⁰(z). Various related identities, many connected to Eisenstein series and some from Ramanujan's lost notebook, are established.

源语言	英语
页（从-至）	13-30
页数	18
期刊	Quarterly Journal of Mathematics
卷	55
期	1
DOI	https://doi.org/10.1093/qmath/hag038
出版状态	已出版 - 3月 2004

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10.1093/qmath/hag038

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abstract = "A new identity for the tenth power of the Dedekind eta-funtion η(z) is established. This is used to give a short proof of Ramanujan's congruence p(11n + 6) ≡ 0 (mod 11) and to prove the lacunarity of η10(z). Various related identities, many connected to Eisenstein series and some from Ramanujan's lost notebook, are established.",

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AB - A new identity for the tenth power of the Dedekind eta-funtion η(z) is established. This is used to give a short proof of Ramanujan's congruence p(11n + 6) ≡ 0 (mod 11) and to prove the lacunarity of η10(z). Various related identities, many connected to Eisenstein series and some from Ramanujan's lost notebook, are established.

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A new identity for (q; q)∞10 with an application to Ramanujan's partition congruence modulo 11

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A new identity for (q; q)_∞¹⁰ with an application to Ramanujan's partition congruence modulo 11