摘要
研究有限域Fq上一类方程βyd1=a1x1d2+a3x3d3+a3x3d4,β,ai∈Fq*,di∈Z+的解数.在保持方程系数不变的前提下,通过对其次数矩阵进行有效降次,可以改进对原方程解数的各种估计.若对方程未知变量和系数进行适当限定,则可将其化为椭圆曲线方程,从而利用Hasse定理得到原方程解数的一个精确界.
We study the number of solutions to the following equation：
βy^d1=α1x2^d2＋α2x2^d3＋α3x3^d4,β,αi∈Fq^＊,di∈Z^＋
While keeping the coefficients unchanged, we effectively .reduce the degree matrix to improve the estimates on the number of solutions to the equation. Furthermore with certain constraint conditions on the variables and coefficients, we obtain a sharp bound on the number of solutions to the equation using Hasse＇s theorem for elliptic curves over finite fields.
出处
《宁波大学学报（理工版）》
CAS
2014年第1期66-69,共4页
Journal of Ningbo University：Natural Science and Engineering Edition
基金
宁波市自然科学基金(2012A610034)
