两类扭Kloosterman和的生成域  

The generating fields of two twisted Kloosterman sums

作　　者：张神星 ZHANG Shenxing(CAS Wu Wen-Tsun Key Laboratory of Mathematics,School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学数学科学学院中科院吴文俊数学重点实验室,安徽合肥230026

出　　处：《中国科学技术大学学报》2021年第12期879-888,共10页JUSTC

基　　金：supported by the NSFC(No.12001510);the Fundamental Research Funds for the Central Universities(No.WK0010000061);Anhui Initiative in Quantum Information Technologies(No.AHY150200)。

摘　　要：研究了扭Kloosterman和Kl(q,a,χ)和部分高斯和g(q,a,χ)的生成域.我们要求特征p相对于χ的阶d充分大,且系数a的迹非零.当p≡±1 mod d时,可以确定这些特征和的生成域.对于一般的p,当a落在底域中时,提出了一个关于(p,d)的组合条件以得到生成域.The generating fields of the twisted Kloosterman sums Kl(q,a,χ)and the partial Gauss sums g(q,a,χ)are studied.We require that the characteristic p is large with respect to the order d of the characterχand the trace of the coefficient a is nonzero.When p≡±1 mod d,we can characterize the generating fields of these character sums.For general p,when a lies in the prime field,we propose a combinatorial condition on(p,d)to ensure one can determine the generating fields.

关 键 词：KLOOSTERMAN和 指数和 分圆域 代数数 

分 类 号：O156.2[理学—数学]