Further improvement on index bounds

Abstract

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index bound given by Wan and Wang. As an application, we give an estimation of the number of all the solutions of some algebraic curves by using our result. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.