Product formulas for the 5-division points on the Tate normal form and the Rogers-Ramanujan continued fraction

DOI10.1016/j.jnt.2018.12.013zbMath1443.11098arXiv1612.06268OpenAlexW2805503076MaRDI QIDQ669236

Patrick Morton

Publication date: 20 March 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06268

zbMATH Keywords

Rogers-Ramanujan continued fraction5-division pointsquintic equationsTate normal formWatson's method

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Continued fractions (11A55)

Related Items (2)

The Hasse invariant of the Tate normal form \(E_5\) and the class number of \(\mathbb{Q}(\sqrt{-5l})\) ⋮ Solutions of Diophantine equations as periodic points of \(p\)-adic algebraic functions. III

Cites Work

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• The cubic Fermat equation and complex multiplication on the Deuring normal form
• Solutions of Diophantine equations as periodic points of \(p\)-adic algebraic functions. I.
• Explicit identities for invariants of elliptic curves
• Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)
• The quartic Fermat equation in Hilbert class fields of imaginary quadratic fields
• The Arithmetic of Elliptic Curves
• Continued fractions and modular functions

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