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The Quarterly Journal of Mathematics 2004 55(1):13-30; doi:10.1093/qmath/hag038
© 2004 by Oxford University Press
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A New Identity for (q;q){infty}10 with an Application to Ramanujan's Partition Congruence Modulo 11

Bruce C. Berndt1, Song Heng Chan1, Zhi-Guo Liu2 and Hamza Yesilyurt3

1 Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA 2 Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China 3 Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA

A new identity for the tenth power of the Dedekind eta-funtion {eta}(z) is established. This is used to give a short proof of Ramanujan's congruence p(11n+6) {equiv}0 (mod 11) and to prove the lacunarity of {eta}10(z). Various related identities, many connected to Eisenstein series and some from Ramanujan's lost notebook, are established.

Received 20 April 2003.


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