Learning outcomes of the course unit
Basic results and techniques of Analytic Number Theory
Basic calculus and algebra
Course contents summary
Distribution of prime numbers: Chebyshev's theorems, Mertens's formulas, Selberg's formulas.
Elementary arithmetical functions: Multiplicative and totally multiplicative functions, Dirichlet product and the hyperbola method.
Sieve Methods: Sketch of Brun's combinatorial sieve and some applications.
The large sieve and its applications.
The Riemann zeta function and some properties, sketch of the analytic proof of the Prime Number Theorem.
Goldbach's problem: additive problems and the circle method.
H. DAVENPORT, Multiplicative Number Theory, terza edizione, Springer, Berlino, 2001.
G. H. HARDY & E. M. WRIGHT, An Introduction to the Theory of Numbers, quinta edizione, Oxford Science Publications, Oxford, 1979.
Assessment methods and criteria
Standard examination: lecture given by the student