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

Scott Ahlgren

doi:10.1090/s0002-9939-99-05181-3

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

Research output: Contribution to journal › Article › peer-review

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 F₂(q), F₃(q), F₄(q), F₅(q), and F₇(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 F₆(q), F₈(q), F₉(q), and F₁₀(q).

Original language	English (US)
Pages (from-to)	1333-1338
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	128
Issue number	5
DOIs	https://doi.org/10.1090/s0002-9939-99-05181-3
State	Published - 2000
Externally published	Yes

Keywords

Ramanujan
Theta functions

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-99-05181-3

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

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