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Elementary and Analytic Theory of Algebraic Numbers
1. Dedekind Domains and Valuations.- 2. Algebraic Numbers and Integers.- 3. Units and Ideal Classes.- 4. Extensions.- 5. P-adic Fields.- 6. Applications of the Theory of P-adic Fields.- 7. AnalyticalExpand
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The Development of Prime Number Theory: From Euclid To Hardy And Littlewood
1. Early Times.- 2. Dirichlet's Theorem on Primes in Arithmetic Progressions.- 3. ?ebysev's Theorem.- 4. Riemann's Zeta-function and Dirichlet Series.- 5. The Prime Number Theorem.- 6. The Turn ofExpand
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Uniform Distribution of Sequences of Integers in Residue Classes
General results.- Polynomial sequences.- Linear recurrent sequences.- Additive functions.- Multiplicative functions.- Polynomial-like functions.
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Global Class-Field Theory
This chapter discusses global class-field theory. The expositions of class-field theory are also presented. The aim of the class-field theory is to describe all abelian extensions of a given field kExpand
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The Prime Number Theorem
The last twenty years of the nineteenth century witnessed a rapid progress in the theory of complex functions, summed up in the monumental treatises of Emile Picard1 (1891–1896) and CamilleExpand
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Classical problems in number theory
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Rational Number Theory in the 20th Century: From PNT to FLT
The Heritage.- The First Years.- The Twenties.- The Thirties.- The Forties and Fifties.- The Last Period.- Fermat's Last Theorem
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An upper bound in Goldbach’s problem
It is clear that the number of distinct representations of a number n as the sum of two primes is at most the number of primes in the interval [n/2, n 2] . We show that 210 is the largest value of nExpand
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Euclidean algorithm in small Abelian fields
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