An estimate on the number of stable quadratic polynomials

In this work we obtain a nontrivial estimate for the size of the set of triples which correspond to stable quadratic polynomials f(X)=aX2+bX+c over the finite field Fq with q odd. This estimate is an improvement of the bound O(q11/4) conjectured in a recent work of A. Ostafe and I. Shparlinski.