UID:
almafu_9959239112502883
Umfang:
1 online resource (392 pages) :
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digital, PDF file(s).
ISBN:
1-139-88402-6
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1-107-36603-8
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1-107-37076-0
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1-107-36112-5
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1-107-36832-4
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1-299-40383-2
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1-107-36357-8
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0-511-66202-5
Serie:
London Mathematical Society lecture note series ; 56
Inhalt:
For a number of years, French mathematicians have run regular number theory conferences to which they have invited number theorists from many countries. To repay their hospitality, the London Mathematical Society arranged for the 1980 'Journees Arithmeiques' to be held in Exeter. The papers published here are either based on the main invited lectures or on selected research talks given at the conference. They cover all branches of the subject: combinatorial and elementary methods; analytic number theory; transcendence theory; Galois module theory and algebraic number theory in general; elliptic curves and modular functions; local fields; additive number theory; Diophantine geometry, and uniform distribution. It will be necessary reading for all those undertaking research in number theory.
Anmerkung:
English or French.
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Cover; Title; Copyright; Contents; PREFACE; ADDRESSES OF CONTRIBUTORS; MAIN SPEAKERS; SPLINTER GROUP SPEAKERS; PARTICIPANTS; Abelian functions and transcendence; 1. PERIODS OF ELLIPTIC INTEGRALS; 2. ABELIAN INTEGRALS; 3. CHARACTERS OF TYPE (A0) AND ZERO ESTIMATES; REFERENCES; Measures of irrationality, transcendence and algebraic independence: recent progress; CHAPTER 1; CHAPTER 2 Measures of the algebraic independence of several numbers. Normal measures of algebraic independence of two numbers connected with elliptic functions; REFERENCES; The Riemann zeta-function; REFERENCES
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On exponential sums and certain of their applications1. INTRODUCTION; 2. DEFINITIONS OF L-FUNCTIONS AND THEIR EQUIVALENCE; 3. PROPERTIES OF POWER SERIES; 4. THE RATIONALITY PRINCIPLE FOR THE L-FUNCTIONS; 5. THE MAGNITUDES OF THE CHARACTERISTIC VALUES: DELIGNE'S THEORY; 6. THE NUMBER OF CHARACTERISTIC VALUES; 7. THE ESTIMATION OF THE EXPONENTIAL SUM WHEN s = 1 and N = 3; 8. VARIANTS OF THE METHOD; 9. THE EXPONENTIAL SUNS IN THE GENERAL CASE; 10. APPLICATIONS OF THE ESTIMATES; REFERENCES; On the calculation of regulators and class numbers of quadratic fields; Introduction
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1. Orders in quadratic fields2. Invertible ideals; 3. Quadratic forms; 4. Reduction; 5. Reduced forms and the class group; 6. The analytic class number formula; 7. Shanks's algorithm for negative discriminants; 8. The group F; 9. The algebraic structure of F; 10. The topological structure of F; 11. Reduced forms in F; 12. Reduction in F; 13. The algorithm for positive discriminants; 14. A numerical example; 15. Concluding remarks; References; Petits discriminants des corps de nombres 151 Stickelberger relations in class groups and Galois module structure; REFERENCES
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Uniform distribution of sequences of integersREFERENCES; Diophantine equations with parameters; 1. Concerning Statement (i); 2. Concerning statement (ii); 3. Concerning statement (iii); 4. Concerning statement (iv); 5. The case s 〉 2.; References; Galois module structure of rings of integers; 1 . HISTORY; 2. GENERAL P1ETHODS; 3. FROHLICH'S CONJECTURE; REFERENCES; On the fractional parts of an3, n and yn; References.; Irregularities of point distribution in unit cubes; References; The Hasse principle for pairs of quadratic forms; 1. MOTIVATIONS; 2. THE CLEAN HASSE PRINCIPLE
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3. SOME WORDS ABOUT THE PROOFREFERENCES; Algorithme d'approximation Diophantienne; RESUME; I. DEFINITION ET PROPRIETIES D'APPROXIMATION; II. ALGDRITHNE; II.1 Existence d'une base d'approximation (n 〉 2); II.2 Methode de calcul (n = 2); II.3 Cas des approximations simultanees; REFERENCE; On the group PSL2(Z{i}); References; Suites a"" faible discrepance en dimension s; 1 INTRODUCTION.; 2 DEFINITIONS ET RESULTATS.; 3 DEFINITION DES SUITES SrRs .; ANNEXE; BIBLIOGRAPHIE; Canonical divisibilities of values of p-adic L-functions; 1. INTRODUCTION AND GENERALITIES; 1. 1 Arithmetic aspects
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1. 2 Analytic results
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English
Weitere Ausg.:
ISBN 0-521-28513-5
Sprache:
Englisch
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