一些同余问题的例外集合  

The exceptional sets of some congruence problems

作　　者：赵瑞 徐哲峰 Zhao Rui;Xu Zhefeng(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2020年第1期26-30,共5页Pure and Applied Mathematics

基　　金：陕西省自然科学基金(2014JM1001).

摘　　要：利用特征和与指数和的估计,研究了一些同余问题的例外集合.具体来说,设p为充分大的素数,集合Y■Zp,正整数N<p.设d为正整数,f(x)为整系数多项式,其次数deg(f)≥2.本文将考虑x在特殊集合中取值,y∈Y时,xy(mod p)的分布情况,还将考虑关于模p剩余系新的表示方式,得到一些同余问题的例外集合的基数估计值.We studied the exceptional sets of some congruence problems by using the estimations of character sums and exponential sums.For details,let p be a large prime,Y■Zp,and let N be a positive integer with N<p.Let d be a positive integer,f(x)be a polynomial with integer coefficients and deg(f)≥2.We will consider the distribution of xy(mod p)when the value of x in a special set,y∈Y.A new representation of the residue classes of modulo p will also be considered.The cardinality of some exceptional sets are given.

关 键 词：同余 剩余系 特征和 指数和 

分 类 号：O156.4[理学—数学]