Let \(\mathbb {F}_q\) be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over \(\mathbb {F}_q \), which extends the results of Wan et al. (Des. Codes Cryptogr. 81, 459–468, 2016) and Wu et al. (Des. Codes Cryptogr. 90, 2813–2821, 2022).

中文翻译：

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有限域上多项式特征和Weil界的改进

令\(\mathbb {F}_q\)为具有q 个元素的有限域，其中q是素数p的幂。在本文中，我们在\(\mathbb {F}_q \)上对与多项式f ( x )相关的字符和的 Weil 界限进行了改进，扩展了 Wan 等人的结果。（Des. Codes Cryptogr. 81 , 459–468, 2016）和 Wu 等人。(Des. Codes Cryptogr. 90 , 2813–2821, 2022)。