Mathematics | University of Parma

Professor: - Alessandro ZACCAGNINI
Academic discipline: Analisi matematica (MAT/05)
Field: Attività formative affini o integrative
Type of training activity: Related/supplementary

48 hours
of face-to-face activities

6 credits

hub:

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

Basic results and techniques of Analytic Number Theory

Prerequisites

Basic calculus and algebra

Course unit content

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.

Full programme

- - -

Bibliography

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.

Teaching methods

Standard class

Assessment methods and criteria

Standard examination: lecture given by the student

Other information