A family of quintic cyclic fields with even class number parameterized by rational points on an elliptic curve

Nakano, Shin

doi:10.1016/j.jnt.2009.04.016

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Infinite Chains Of Discriminant-preserving Transformations1

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Cited by 2 publications

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“…To conclude this section, we observe that the above parametric forms share properties similar to a celebrated parametrized family of quintics, found by Emma Lehmer 39,40 to provide connections between the so-called Gaussian period equations and cyclic units. For instance, in the notation of Butler and McKay 41 , their common Galois group is 5T1.…”

Section: Infinite Chains Of Discriminant-preserving Transformationssupporting

confidence: 53%

Equivalence among orbital equations of polynomial maps

Gallas

2018

Int. J. Mod. Phys. C

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This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic, valid for arbitrary dynamics governed by algebraic equations of motion.

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Section: Infinite Chains Of Discriminant-preserving Transformationssupporting

confidence: 53%