有限域上多项式的指数和及其L-函数Exponential sums and L-functions of polynomials over finite fields
韩山猛;祝美玲;曹炜;
摘要(Abstract):
L-函数蕴藏着深刻的算术信息,是数论中重要的研究对象.有限域上多项式的指数和及其L-函数在一般情形下难以计算.通过利用高斯和及多项式的次数矩阵的Smith标准形,得到了在特定情形下有限域上一类多项式的指数和及其L-函数的具体公式.
关键词(KeyWords): 有限域;Smith标准形;指数和;L-函数
基金项目(Foundation): 国家自然科学基金(11371208);; 宁波市自然科学基金(2016A610079)
作者(Authors): 韩山猛;祝美玲;曹炜;
参考文献(References):
- [1]冯克勤,廖群英.有限域及其应用[M].大连:大连理工大学出版社,2011.
- [2]Lidl R,Niederreiter H.Finite Fields[M].Cambridge UK:Cambridge Univ Press,1997.
- [3]Schmidt W M.Equations over Finite Fields:An Elementary Approach[M].New York:Springer-Verlag,1976.
- [4]Ax J.Zeros of polynomials over finite fields[J].Amer J Math.,1964,2:255-261.
- [5]Wang W S,Sun Q.The number of solutions of certain equations over finite fields[J].Finite Fields Appl.,2005,2:182-192.
- [6]Cao W,Sun Q.On a class of equations with special degrees over finite fields[J].Acta Arith.,2007,130:195-202.
- [7]Cao W.Smith normal form of augmented degree matrix and its applications[J].Linear Algebra Appl.,2009,431:1778-1784.
- [8]Chen J M,Cao W.Smith normal form of augmented degree matrix and rational points on toric hypersurface[J].Algebra Colloq.,2013,20:327-332.
- [9]Hong S F.L-functions of twisted diagonal exponential sums over finite fields[J].Proc.Amer.Math.Soc.,2007,135:3099-3108.
- [10]Smith J S.On systems of linear indeterminate equations and congruences[J].Philos.Trans.Royal.Soc.London,1861,151:293-326.
- [11]Berndt B,Evans R,Williams K.Gauss and Jacobi Sums[M].New Yock:Wiley Interscience,1998.
- [12]陈国华,武艳丽,张艳娜.某种特定类型三角和的定量估计[J].纯粹数学与应用数学,2013,29:325-330.
- [13]Adolphson A,Sperber S.Exponential sums and Newton polyhedra:cohomology and estimates[J].Ann.Math.,1989,130:367-406.
- [14]Adolphson A,Sperber S.Newton polyhedra and the degree of the L-function associated to an exponential sum[J].Invent Math.,1987,88:555-569.