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math.NT2023
On sums of powers of consecutive squares over finite fields, and sums of distinct values of polynomials
Zhiguo Ding, Michael E. Zieve
For each odd prime power q, and each integer k, we determine the sum of the k-th powers of all elements x in F_q for which both x and x+1 are squares in F_q^*. We also solve the an…
math.NT2023
Constructing permutation polynomials using generalized Redei functions
Zhiguo Ding, Michael E. Zieve
We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class o…
math.NT2023
Roots of certain polynomials over finite fields
Zhiguo Ding, Michael E. Zieve
We determine the roots in F_{q^3} of the polynomial X^{2q^k+1} + X + c for each positive integer k and each c in F_q, where q is a power of 2. We introduce a new approach for this…