OVERVIEW

The course will give an introduction to analytic number theroy.

The lecture will be in Italian unless requested otherwise by the students.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to introduce basic elementary and analytical concepts, and the relative techniques, for the study of arithmetic problems, in particular concerning prime numbers. The course provides analytical prerequisites necessary to address more advanced issues in Number Theory, Arithmetic Geometry and related topics.

PREREQUISITES

It is useful to have some basic knowledge of complex analysis.

TEACHING METHODS

Traditional

SYLLABUS/CONTENT

Arithmetical functions: arithmetical and algebraic aspects, asymptotic behavior. Elementary methods for the distribution of primes: Euler, Legendre and Chebyshev. Elements of cryptography. Complements of Analysis: Dirichlet series, Mellin transform and Poisson formula. Riemann zeta function: general properties and distribution of zeros. Prime Number Theorem: explicit formulae and PNT with remainder. Dirichlet L-functions: Dirichlet characters, general properties of L-functions and distribution of zeros. Dirichlet's theorem.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes.

A.E.Ingham - The Distribution of Prime Numbers - Cambridege U.P. 1964.

H.Davenport - Multiplicative Number Theory - Springer 1980.

G.Tenenbaum, M.Mendes-France - The Prime Numbers and Their Distribution - AMS 2000.

G.Tenenbaum - Introduction to Analytic and Probabilistic Number Theory - Cambridge U.P., 1995

TEACHERS AND EXAM BOARD

Exam Board

SANDRO BETTIN (President)

MARC ALEXANDRE MUNSCH

ALBERTO PERELLI (President Substitute)

LESSONS

Class schedule

L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.

EXAMS

EXAM DESCRIPTION

Written and oral exam

ASSESSMENT METHODS

Written exam and oral exam on parts of the program

Exam schedule