Stable polynomials over finite fields | Zendy

Domingo GómezPérez | Zendy; Alejandro P. Nicolás | Zendy; Alina Ostafe | Zendy; Daniel Sadornil | Zendy

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Stable polynomials over finite fields

Author(s) -

Domingo GómezPérez,

Alejandro P. Nicolás,

Alina Ostafe,

Daniel Sadornil

Publication year - 2014

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/791

Subject(s) - finite field , mathematics , pure mathematics , algebra over a field , discrete mathematics

We use the theory of resultants to study the stability, that is, the property of having all iterates irreducible, of an arbitrary polynomial f over a finite field Fq. This result partially generalizes the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for p = 3, we show that certain polynomials of degree three are not stable. We also use the Weil bound for multiplicative character sums to estimate the number of stable polynomials over a finite field of odd characteristic

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