CODE  84023 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
TEACHING LOCATION 

SEMESTER  1° Semester 
TEACHING MATERIALS  AULAWEB 
The course will give an introduction to analytic number theroy.
The lecture will be in Italian unless requested otherwise by the students.
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.
It is useful to have some basic knowledge of complex analysis.
Traditional
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 Lfunctions: Dirichlet characters, general properties of Lfunctions 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.MendesFrance  The Prime Numbers and Their Distribution  AMS 2000.
G.Tenenbaum  Introduction to Analytic and Probabilistic Number Theory  Cambridge U.P., 1995
Office hours: By appointment
SANDRO BETTIN (President)
MARC ALEXANDRE MUNSCH
ALBERTO PERELLI (President Substitute)
All class schedules are posted on the EasyAcademy portal.
Written and oral exam
Written exam and oral exam on parts of the program
Date  Time  Location  Type  Notes 

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 