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A PAGE ON EISENSTEIN SERIES IN RAMANUJAN'S LOST NOTEBOOK

Published online by Cambridge University Press:  01 May 2003

BRUCE C. BERNDT  and
AE JA YEE
BRUCE C. BERNDT
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA e-mail: [email protected], [email protected]
AE JA YEE
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA e-mail: [email protected], [email protected]
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Abstract

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Page 188 in Ramanujan's lost notebook is devoted to a certain class of infinite series connected with Euler's pentagonal number theorem. These series are represented in terms of Ramanujan's famous Eisenstein series $P, Q$, and $R$. The purpose of this paper is to prove all the formulas on page 188 and to show that one of them leads to an interesting, new recurrence formula for $\sigma (n)$, the sum of the positive divisors of $n$.

Keywords

11F11
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 123 - 129
Copyright
2003 Glasgow Mathematical Journal Trust