费马大定理笔记(英文)/他山之石系列/国外优秀数学著作原版系列
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作者(澳)阿尔弗·范·德·普尔坦恩|责编:杜莹雪//李烨
出版社哈尔滨工业大学
ISBN9787560393612
出版时间2021-03
装帧平装
开本其他
定价48元
货号31147303
上书时间2023-08-29
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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.
内容摘要
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。本书适合高等院校师生、研究生及数学爱好者参考阅读。
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