CODE 84023 2022/2023 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA MAT/05 GENOVA 1° Semester AULAWEB

## 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.

### 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.

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

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

Written and oral exam

### ASSESSMENT METHODS

Written exam and oral exam on parts of the program

### Exam schedule

Data appello Orario Luogo Degree type Note
10/01/2023 09:30 GENOVA Scritto
12/01/2023 14:30 GENOVA Orale
31/01/2023 09:30 GENOVA Scritto
02/02/2023 14:30 GENOVA Orale
08/06/2023 09:30 GENOVA Scritto
08/06/2023 14:30 GENOVA Orale
06/07/2023 09:30 GENOVA Scritto
06/07/2023 14:30 GENOVA Orale
14/09/2023 09:30 GENOVA Scritto
14/09/2023 14:30 GENOVA Orale