Several \(q\)-series related to Ramanujan's theta functions

DOI10.1007/s11139-019-00187-4zbMath1467.33013arXiv1812.06458OpenAlexW2990549994MaRDI QIDQ829854

Ernest X. W. Xia, Dazhao Tang

Publication date: 6 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.06458

zbMATH Keywords

Ramanujan's theta functionsJacobi's triple product identity\(q\)-series expansionsinterlinked identities

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences for modular and (p)-adic modular forms (11F33)

Related Items

Results on vanishing coefficients in infinite \(q\)-series expansions for certain arithmetic progressions mod 7 ⋮ Vanishing coefficients in three families of products of theta functions ⋮ Results on vanishing coefficients in certain infinite \(q\)-series expansions ⋮ Vanishing coefficients in powers of theta functions with odd moduli ⋮ Distribution and divisibility of the Fourier coefficients of certain Hauptmoduln ⋮ Vanishing coefficients in three families of products of theta functions. II ⋮ New infinite \(q\)-product expansions with vanishing coefficients ⋮ Asymptotics for the Taylor coefficients of certain infinite products ⋮ 5-dissections and sign patterns of Ramanujan's parameter and its companion ⋮ Generalizations of Hirschhorn’s Results on Two Remarkable q-Series Expansions

Cites Work

• Unnamed Item
• Some results on vanishing coefficients in infinite product expansions
• On the crank function of cubic partition pairs
• The power of \(q\). A personal journey
• Two remarkable \(q\)-series expansions
• Ramanujan's Theta Functions
• Vanishing coefficients in some q-series expansions