Incomplete Character Sums and a Special Class of Permutations

Sum-Product and Character Sums in finite fields

In this talk I will present estimates on incomplete character sums in finite fields, with special emphasize on the non-prime case. Some of the results are of the same strength as Burgess celebrated theorem for prime fields. The improvements are mainly based on arguments from arithmetic combinatorics providing new bounds on multiplicative energy and an improved amplification strategy. In particu...

Large Partial Random Permutations of Conditionally Convergent Series

This paper studies the behavior of sums of series under random permutations. The first result considers the case of uniformly distributed permutations on the set N of all integers, which requires finitely additive probability. The next result considers the limit of the first portion p, 0 ≤ p ≤ 1, of a uniform distribution on the first n integers, as n gets large. The focal point is when 0 < p <...

Character Sums and Ramsey Properties of Generalized Paley Graphs

In a classic paper, Evans, Pulham, and Sheehan computed the number of complete graphs of size 4 for a special class of graphs called Paley Graphs. Here we consider analogous questions for generalized Paley-type graphs.

An Estimate of Incomplete Mixed Character Sums

On the weight distributions of a class of cyclic codes

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases in [14, 15, 16]. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special case. We make extensive use of standard tools in number theory such as characters of finite fields, the Gauss sums and the Jacobi sums to tra...