An estimate on the number of stable quadratic polynomials

  • Authors:

  • Domingo Gomez;Alejandro P. NicoláS

  • Affiliations:

  • Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain;Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2010

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Abstract

In this work we obtain a nontrivial estimate for the size of the set of triples (a,b,c)@?F"q^*xF"qxF"q which correspond to stable quadratic polynomials f(X)=aX^2+bX+c over the finite field F"q with q odd. This estimate is an improvement of the bound O(q^1^1^/^4) conjectured in a recent work of A. Ostafe and I. Shparlinski.