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. Analytical… Expand

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 of… Expand

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 k… Expand

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 Camille… Expand

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 n… Expand