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A PAGE ON EISENSTEIN SERIES IN RAMANUJAN'S LOST NOTEBOOK
Published online by Cambridge University Press: 01 May 2003
Abstract
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 $n$.
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- Research Article
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- 2003 Glasgow Mathematical Journal Trust
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