A page on Eisenstein series in Ramanujan's lost notebook

Bruce C. Berndt, Ae Ja Yee

Research output: Contribution to journalArticle

10 Scopus citations

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 σ(n), the sum of the positive divisors of n.

Original languageEnglish (US)
Pages (from-to)123-129
Number of pages7
JournalGlasgow Mathematical Journal
Volume45
Issue number1
DOIs
StatePublished - Jan 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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