The sixth, eighth, ninth, and tenth powers of ramanujan's theta function

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Abstract

In his Lost Notebook, Ramanujan claimed that the "circular" summation of the n-th powers of the symmetric theta function f(a, b) satisfies a factorization of the form f(a, b)F n(ab). Moreover, Ramanujan recorded identities expressing F 2(q), F 3(q), F 4(q), F 5(q), and F 7(q) in terms of his theta functions φ(q), ψ(q), and f(-q). Ramanujan's claims were proved by Rangachari, and later (via elementary methods) by Son. In this paper we obtain similar identities for F 6(q), F 8(q), F 9(q), and F 10(q).

Original languageEnglish (US)
Pages (from-to)1333-1338
Number of pages6
JournalProceedings of the American Mathematical Society
Volume128
Issue number5
StatePublished - 2000
Externally publishedYes

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Keywords

  • Ramanujan
  • Theta functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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