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Arithmetic Properties of Generalized Rikuna Polynomials

Z. ChonolesJ. CullinanH. HausmanA.M. PacelliS. PegadoF. Wei — 2014

Publications mathématiques de Besançon

Fix an integer 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order , where K satisfies some mild hypotheses. In this paper we define the family of { r n ( x , t ) } n 1 of degree n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd over an arbitrary base field and give applications to arithmetic dynamical systems.

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