13 lectures on Fermat's last theorem
著者
書誌事項
13 lectures on Fermat's last theorem
Springer-Verlag, c1979
- : us
- : gw
- タイトル別名
-
Thirteen lectures on Fermat's las theorem
大学図書館所蔵 全64件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographies and indexes
内容説明・目次
内容説明
Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history , as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue- eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy.
Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.
目次
Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naive Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Congruences.- 4 Wendt's Theorem.- 5 Abel's Conjecture.- 6 Fermat's Equation with Even Exponent.- 7 Odds and Ends.- Lecture V Kummer's Monument.- 1 A Justification of Kummer's Method.- 2 Basic Facts about the Arithmetic of Cyclotomic Fields.- 3 Kummer's Main Theorem.- Lecture VI Regular Primes.- 1 The Class Number of Cyclotomic Fields.- 2 Bernoulli Numbers and Kummer's Regularity Criterion.- 3 Various Arithmetic Properties of Bernoulli Numbers.- 4 The Abundance of Irregular Primes.- 5 Computation of Irregular Primes.- Lecture VII Kummer Exits.- 1 The Periods of the Cyclotomic Equation.- 2 The Jacobi Cyclotomic Function.- 3 On the Generation of the Class Group of the Cyclotomic Field.- 4 Kummer's Congruences.- 5 Kummer's Theorem for a Class of Irregular Primes.- 6 Computations of the Class Number.- Lecture VIII After Kummer, a New Light.- 1 The Congruences of Mirimanoff.- 2 The Theorem of Krasner.- 3 The Theorems of Wieferich and Mirimanoff.- 4 Fermat's Theorem and the Mersenne Primes.- 5 Summation Criteria.- 6 Fermat Quotient Criteria.- Lecture IX The Power of Class Field Theory.- 1 The Power Residue Symbol.- 2 Kummer Extensions.- 3 The Main Theorems of Furtwangler.- 4 The Method of Singular Integers.- 5 Hasse.- 6 The p-Rank of the Class Group of the Cyclotomic Field.- 7 Criteria of p-Divisibility of the Class Number.- 8 Properly and Improperly Irregular Cyclotomic Fields.- Lecture X Fresh Efforts.- 1 Fermat's Last Theorem Is True for Every Prime Exponent Less Than 125000.- 2 Euler Numbers and Fermat's Theorem.- 3 The First Case Is True for Infinitely Many Pairwise Relatively Prime Exponents.- 4 Connections between Elliptic Curves and Fermat's Theorem.- 5 Iwasawa's Theory.- 6 The Fermat Function Field.- 7 Mordell's Conjecture.- 8 The Logicians.- Lecture XI Estimates.- 1 Elementary (and Not So Elementary) Estimates.- 2 Estimates Based on the Criteria Involving Fermat Quotients.- 3 Thue, Roth, Siegel and Baker.- 4 Applications of the New Methods.- Lecture XII Fermat's Congruence.- 1 Fermat's Theorem over Prime Fields.- 2 The Local Fermat's Theorem.- 3 The Problem Modulo a Prime-Power.- Lecture XIII Variations and Fugue on a Theme.- 1 Variation I (In the Tone of Polynomial Functions).- 2 Variation II (In the Tone of Entire Functions).- 3 Variation III (In the Theta Tone).- 4 Variation IV (In the Tone of Differential Equations).- 5 Variation V (Giocoso).- 6 Variation VI (In the Negative Tone).- 7 Variation VII (In the Ordinal Tone).- 8 Variation VIII (In a Nonassociative Tone).- 9 Variation IX (In the Matrix Tone).- 10 Fugue (In the Quadratic Tone).- Epilogue.- Index of Names.
「Nielsen BookData」 より