13 Lectures on Fermat’s Last Theorem / by Paulo Ribenboim
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York |
| 出版年 | 1979 |
| 本文言語 | 英語 |
| 大きさ | XVI, 302 p : online resource |
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| 内容注記 | 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 Naïve 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 Furtwängler 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 |
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| 著者標目 | *Ribenboim, Paulo author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Computer science LCSH:Number theory FREE:Mathematics FREE:Number Theory FREE:Computer Science, general |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9781468493429 
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| ISBN | 9781468493429 |
| URL | http://dx.doi.org/10.1007/978-1-4684-9342-9 |
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