作者：（美）W.M.施密特
页数：267
出版社：世界图书出版公司
出版日期：2017
ISBN：9787519229283
电子书格式：pdf/epub/txt
内容简介
由W.M.施密特著的《有限域上的方程(英文版)》是Springer“数学讲义丛书”之536卷，作者是美国科罗拉多州立大学数学系教授，本书基于M.Ratliff和K.Spackman在该校授课的讲义编写而成。本书由浅入深，以最简单的曲线方程yd=f(x)开篇，全面介绍了有限域上的各种方程。读者对象：数学专业的研究生和科研工作者.
作者简介
本书作者Wolfgang M. Schmidt (W. M. 施密特) 是美国科罗拉多州立大学数学系知名教授，本书基于M.Ratliff和K.Spackman在该校授课的讲义编写而成。
本书特色
本书是Springer“数学讲义丛书”之536卷，作者是美国科罗拉多州立大学数学系教授，本书基于M.Ratliff和K.Spackman在该校授课的讲义编写而成。本书由浅入深，以最简单的曲线方程yd=f(x)开篇，全面介绍了有限域上的各种方程。读者对象：数学专业的研究生和科研工作者.
目录
Introduction
I.Equations yd=f(x)and yq-y=f(x)
1.Finite Fields
2.Equations yd=t(x)
3.Construction of certain polynomiale
4.Proof of the Main Theorem
5.Removal of the condition (m,d)=1
6.Hyperderivatives
7.Removal of the condition that q=p or p2 .
9.Equations yq-y=f(x)
II.Character Sums and Exponential Sums
1.Characters of Finite Abelian Groups
2.Characters and Character Sums associated with Finite Flelds
3.Gaussian sums
4.The low road.
5.Systems of equations y1d1=f1(x), ,yndn=fn（x）.
6.Auxiliary lemmas on wv1+…+□
7.Further auxillary lemmas
8.Zeta Function and L-Functions
9.special L-Functions
10.Fleld extengiong.The Davenport-Hasse relations
11.Proof of the Principal Theorems
12.Kloosterman Sums
13.Further Results
III.Abeolutoly Irreducible Equatione f(x,y)=0
1.Introduction
2.Independence results
3.Derivatives.
4.Construction of two algebraic functions
5.Constructlon of two polynomlals
6.Proof of the Main Theorem
8.Hyperderivatives again
9.Removal of the condition that q=p
IV.Equations in Many Variables
1.Theorems of Chevalley and Warning
2.Quadratic forms
3.Elementary upper bounds.Projective zeros
4.The average number of zeros of a polynomial
5.Additive Bquatione:A Chebychev Argument
6.Additive Equations:Character Sums
7.Bquations f,(y）x,l1+ +f(y）xn=o
V.Absolutely Irreducible squations f(x,.…,x)=0
1.Elimination Theory
2.The absolute irreducibility of polynomlals(I)
3.The abaolute irreducibllity of polynomial8(II)
4.The absolute 1rreducibility of polynomlals(III)
5.The number of zeroe of abaolutely irreducib1e polynomiale in n varlables
VI.Rudimente of Algebraic Goometry,The Number of Pointa in Varieties over Finite Fields
1.Varietoes
2.Dimension
3.Rational Maps
4.BirationalMaps
5.Linear Disjointness of Fields
6.Constant Field Extensions
7.Counting Points in Varieties Over Finite Pields
I.Equations yd=f(x)and yq-y=f(x)
1.Finite Fields
2.Equations yd=t(x)
3.Construction of certain polynomiale
4.Proof of the Main Theorem
5.Removal of the condition (m,d)=1
6.Hyperderivatives
7.Removal of the condition that q=p or p2 .
9.Equations yq-y=f(x)
II.Character Sums and Exponential Sums
1.Characters of Finite Abelian Groups
2.Characters and Character Sums associated with Finite Flelds
3.Gaussian sums
4.The low road.
5.Systems of equations y1d1=f1(x), ,yndn=fn（x）.
6.Auxiliary lemmas on wv1+…+□
7.Further auxillary lemmas
8.Zeta Function and L-Functions
9.special L-Functions
10.Fleld extengiong.The Davenport-Hasse relations
11.Proof of the Principal Theorems
12.Kloosterman Sums
13.Further Results
III.Abeolutoly Irreducible Equatione f(x,y)=0
1.Introduction
2.Independence results
3.Derivatives.
4.Construction of two algebraic functions
5.Constructlon of two polynomlals
6.Proof of the Main Theorem
8.Hyperderivatives again
9.Removal of the condition that q=p
IV.Equations in Many Variables
1.Theorems of Chevalley and Warning
2.Quadratic forms
3.Elementary upper bounds.Projective zeros
4.The average number of zeros of a polynomial
5.Additive Bquatione:A Chebychev Argument
6.Additive Equations:Character Sums
7.Bquations f,(y）x,l1+ +f(y）xn=o
V.Absolutely Irreducible squations f(x,.…,x)=0
1.Elimination Theory
2.The absolute irreducibility of polynomlals(I)
3.The abaolute irreducibllity of polynomial8(II)
4.The absolute 1rreducibility of polynomlals(III)
5.The number of zeroe of abaolutely irreducib1e polynomiale in n varlables
VI.Rudimente of Algebraic Goometry,The Number of Pointa in Varieties over Finite Fields
1.Varietoes
2.Dimension
3.Rational Maps
4.BirationalMaps
5.Linear Disjointness of Fields
6.Constant Field Extensions
7.Counting Points in Varieties Over Finite Pields
