INTRODUCTION TO THE ANALYTIC THEORY OF NUMBERS
Learning outcomes of the course unit
An overview of the most important problems of the
Functions of one variable A and B, Topology and complex variable
Course contents summary
1. Distribution of prime numbers: Chebyshev’s theorems, Mertens formulae, Selberg’s formulae.
2. Basic arithmetic functions, multiplicative functions and completely multiplicative functions, Dirichlet product and hyperbola method.
3. Sieve methods: mention of Brun’s combinatorial sieve and its applications.
4. The large sieve and a few applications.
5. Riemann zeta function and its properties, mention of the analytical demonstration of the Prime Number Theorem.
6. Mention of the Goldbach problem and the circle method.
1. T. M. APOSTOL, Introduction to Analytic Number Theory,Springer, Berlino, 1975.
2. K. CHANDRASEKHARAN, Introduction to Analytic Number Theory,Springer, Berlino, 1968.
3. H. DAVENPORT, Multiplicative Number Theory, terza edizione,Springer, Berlino, 2001.
4. G. H. HARDY & E. M. WRIGHT,An Introduction to the Theory of Numbers, fifth edition, Oxford Science Publications, Oxford, 1979.
5. L. K. HUA, Introduction to Number Theory, Springer, Berlino, 1982.
6. E. LANDAU, Elementary Number Theory, Chelsea, New York, 1960.