Solving polynomial equations with elliptic modular functions

Daniel Phillip Schultz

Research output: Contribution to journalArticle

Abstract

Klein's method of solving algebraic equations is discussed and generalized to provide conditions for the unnecessity of the so-called accessory irrationality. We use the modular curve of level N to produce a "hyper-radical" of level N and discuss the accessory irrationalities involved in solving polynomial equations by means of the algebraic hypergeometric functions that define this hyper-radical. The quintic normal forms of Brioschi and Hermite elegantly fit into this framework, and we find explicit conditions for the unnecessary of accessory irrationalities for these normal forms.

Original languageEnglish (US)
Pages (from-to)1313-1344
Number of pages32
JournalInternational Journal of Number Theory
Volume11
Issue number4
DOIs
StatePublished - Jun 5 2015

Fingerprint

Irrationality
Modular Functions
Elliptic function
Polynomial equation
Normal Form
Modular Curves
Algebraic function
Quintic
Hypergeometric Functions
Hermite
Algebraic Equation

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Schultz, Daniel Phillip. / Solving polynomial equations with elliptic modular functions. In: International Journal of Number Theory. 2015 ; Vol. 11, No. 4. pp. 1313-1344.
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Solving polynomial equations with elliptic modular functions. / Schultz, Daniel Phillip.

In: International Journal of Number Theory, Vol. 11, No. 4, 05.06.2015, p. 1313-1344.

Research output: Contribution to journalArticle

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