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Introduction to Analytic and Probabilistic Number Theory

2015; American Mathematical Society; Linguagem: Inglês

10.1090/gsm/163

2376-9203

Gérald Tenenbaum,

History and Theory of Mathematics

Elementary methods Some tools from real analysis Prime numbers Arithmetic functions Average orders Sieve methods Extremal orders The method of van der Corput Diophantine approximation Complex analysis methods The Euler gamma function Generating functions: Dirichlet series Summation formulae The Riemann zeta function The prime number theorem and the Riemann hypothesis The Selberg-Delange method Two arithmetic applications Tauberian theorems Primes in arithmetic progressions Probabilistic methods Densities Limiting distributions of arithmetic functions Normal order Distribution of additive functions and mean values of multiplicative functions Friable integers The saddle-point method Integers free of small factors Bibliography Index