The course will give an introduction to analytic number theroy.
The lecture will be in Italian unless requested otherwise by the students.
AM1, AM2, AM3, ALGA, Algebra 1 e 2, Geometria.
It is useful but not essential to have followed Analisi Complessa.
In presence
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: explicit formulae and Dirichlet's theorem with remainder.
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
Ricevimento: By appointment
SANDRO BETTIN (President)
STEFANO VIGNI
ALBERTO PERELLI (President Substitute)
Written and oral exam
Written exam and oral exam on parts of the program
