函数域中与相交多项式相关的计数估计  

Counting estimates related to intersective polynomials in function fields

作　　者：吴家淼 蔺玉荣 李国全[1] 许贵桥[1] WU Jiamiao;LIN Yurong;LI Guoquan;XU Guiqiao(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2024年第2期1-5,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11671271).

摘　　要：设F_(q)[t]为q个元的有限域F_(q)上的多项式环,设h∈F_(q)[t][x]为一个相交多项式,A■F_(q)[t]为由一些次数小于N的多项式构成的集合.利用密度增量估计构造4元组序列,当A的密度适当大时,得到了方程x-y=z解数的估计,其中:x、y∈A,z∈h(F_(q)[t])\{0}.Let F_(q)[t]denote the polynomial ring over the finite field F_(q)of q elements,h∈F_(q)[t][x]is an intersective polynomial,A■F_(q)[t]is a set containing some polynomials of degree less than N.A sequence of group with four elements is constructed by estimation of density increment.When the density of A is sufficiently large,the estimation of number of solutions to the equation x-y=z is obtained,where x,y∈A and z∈h(F_(q)[t])\{0}.

关 键 词：多项式环 相交多项式 FOURIER分析 密度增量 

分 类 号：O156[理学—数学]