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- ISBN:9787560393612
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:24cm
- 页数:325页
- 出版时间:2021-03-01
- 条形码:9787560393612 ; 978-7-5603-9361-2
内容简介
本书阐述了带有历史性质的介绍、关于唯一因子分解的说明、初等数论方法等有关内容。本书主要包括曲线、模形式、模块性猜想、函数方程、Zeta函数和L-级数、ABC猜想、带有历史性质的介绍、关于唯一因子分解的说明、初等数论方法、库默尔参数、丢番图和费马、一个孩子对椭圆函数的介绍、局部与全局、虚二次数域的类数、威利的证明、有关费马大定理的摘要、达尔蒙和格兰维尔的广义费马函数等内容。
目录
Quasi-historical introduction
The cases n =2 and n =4.The Parisian Academy in the 1840s.
Notes: Some details. Descent.Algebraic numbers and integers.
Remarks on unique factorizationA digression.
Notes:Continued fractions.Plagiarism.
Elementary methods
Sophie Germain, Abel's formulas, Mirimanoff-Wieferich,..
Notes: Fermat's Theorem.Bernoulli numbers. Euler-Maclaurin.
Pseudoprimes. Fermat numbers. Mersenne primes. Cranks.
Kummer's arguments
Proof of the FLT for regular primes.
Notes: Some remarks for undergraduates on elementary algebra.
Equivalence relations.
Why do we believe Wiles? More quasi-historyRantings. Work on the FLT this century.
Notes: Euler's conjecture. The growing of the "gap”.
Diophantus and Fermat
What the study of diophantine equations is really all about.
Notes: The chord and tangent method.Examples.
A child's introduction to elliptic functions
For a precocious child.
Notes: Discriminants.
Local and global
Some remarks on p-adic numbers.
Notes: The Riemann C-function.Much more on p-adic numbers.
Curves
Particularly,about elliptic curves.
Notes: Minimal model. Semisimplicity of the Frey curve.
Birational equivalence.
Modular forms
Some formulas and assertions.
Notes: More formulas.The discriminant function.
The Modularity ConjectureAn attempt at an explanation.
Notes: What's in a name?
The functional equation
Poisson summation: 9-functions.
Notes: Details. Hecke operators.
Zeta functions and L-series
Introduction to the Birch-Swinnerton-Dyer Conjectures.
Notes: Hasse's Theorem.
The ABC-Conjecture
Darmon and Granville's Generalized Fermat Equation.
Notes: Hawkins primes.The Generalized Fermat Conjecture.
Heights
Remarks on the Mordell-Weil Theorem.
Notes: Lehmer's Question. Elliptic curves of high rank.
Class number of imaginary quadratic number fieldsThe proof of Goldfeld-Gross-Zagier.
Notes: Composition of quadratic forms. Tate-Shafarevitch group.
Jacobian. Heegner points.
Wiles'proof
Not the commutative algebra, of course.
Notes: Some details.
Appendices
Remarks on Fermat's Last Theorem
For those who only want to pretend to have read the rest of this book.
"The Devil and Simon Flagg", by Arthur PorgesThe devil fails where Wiles will succeed.
“Math Riots Prove Fun Incalculable",by Eric ZornIs the FLT truly as important as sport?
Index
编辑手记
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