2010/02/03 by Ke Гонг, Gong, Ke
Computer Science · Mathematics · #11L26 #11L40 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1002.0670
openalex publication_date 2010/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize Burgess' results on partial Gaussian sums to arbitrary finite fields. The main ingredients are the classical method of amplification, two deep results on multiplicative energy for subsets in finite fields which are obtained respectively by the tools from additive combinatorics and geometry of numbers, and a technique of Chamizo for treating the difficulty caused by additive character. Our results include the recent works on character sums in finite fields by M.-C. Chang and S. V. Konyagin.