Can I read On Sums of Powers of Consecutive Squares Over Finite Fields, and Sums of Distinct Values of Polynomials on EtoBox?

On Sums of Powers of Consecutive Squares Over Finite Fields, and Sums of Distinct Values of Polynomials by Ding, Zhiguo; Zieve, Michael E. is a scholarly article available to read on EtoBox.

What is On Sums of Powers of Consecutive Squares Over Finite Fields, and Sums of Distinct Values of Polynomials about?

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 analogous problem when one or both of x and x+1 is a nonsquare. We use these results to determine the sum of the elements of the image set f(F_q) for each f(X) in F_q[X] of the form X^4+aX^2+b, which resolves two conjectures by Finch-Smith, Harrington, and Wong.

Author

Ding, Zhiguo; Zieve, Michael E.

Published

2023

Language

EN