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Springer New York


438,86 PLN
Wysyłamy w 28 dni

Opis produktu

Lecture I The Early History of Fermats Last Theorem. 1 The Problem. 2 Early Attempts. 3 Kummers Monumental Theorem. 4 Regular Primes. 5 Kummers 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 Fermats Equation of Degree Seven. Lecture IV The Na > ve Approach. 1 The Relations of Barlow and Abel. 2 Sophie Germain. 3 Congruences. 4 Wendts Theorem. 5 Abels Conjecture. 6 Fermats Equation with Even Exponent. 7 Odds and Ends. Lecture V Kummers Monument. 1 A Justification of Kummers Method. 2 Basic Facts about the Arithmetic of Cyclotomic Fields. 3 Kummers Main Theorem. Lecture VI Regular Primes. 1 The Class Number of Cyclotomic Fields. 2 Bernoulli Numbers and Kummers 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 Kummers Congruences. 5 Kummers 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 Fermats 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 FurtwĄngler. 4 The Method of Singular Integers. 5 Hasse. 6 The pRank of the Class Group of the Cyclotomic Field. 7 Criteria of pDivisibility of the Class Number. 8 Properly and Improperly Irregular Cyclotomic Fields. Lecture X Fresh Efforts. 1 Fermats Last Theorem Is True for Every Prime Exponent Less Than 125000. 2 Euler Numbers and Fermats Theorem. 3 The First Case Is True for Infinitely Many Pairwise Relatively Prime Exponents. 4 Connections between Elliptic Curves and Fermats Theorem. 5 Iwasawas Theory. 6 The Fermat Function Field. 7 Mordells 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 Fermats Congruence. 1 Fermats Theorem over Prime Fields. 2 The Local Fermats Theorem. 3 The Problem Modulo a PrimePower. 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

Wymiary: 1420 gr 156 mm 234 mm

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