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

^*Corresponding author for this work

School of Mathematical Sciences

University of Illinois Urbana–Champaign

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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.

Original language	English
Pages (from-to)	13-30
Number of pages	18
Journal	Quarterly Journal of Mathematics
Volume	55
Issue number	1
DOIs	https://doi.org/10.1093/qmath/hag038
State	Published - Mar 2004

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

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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AU - Berndt, Bruce C.

AU - Chan, Song Heng

AU - Liu, Zhi Guo

AU - Yesilyurt, Hamza

PY - 2004/3

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N2 - 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.

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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M3 - 文章

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JO - Quarterly Journal of Mathematics

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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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