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Let q > 2 be a prime power and , where . We prove that f is a permutation polynomial of if and only if one of the following occurs: (i) q is even and ; (ii) q ≡ 1 (mod 8) and t² = -2.
In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type , where q is a power of p.
In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem:
where denotes the number of monic irreducible polynomials in with norm .
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