401-3109-65L  Probabilistic Number Theory

SemesterHerbstsemester 2015
DozierendeE. Kowalski
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThe course presents some aspects of probabilistic number theory, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums.
Lernziel
InhaltThe goal of the course is to present some results of probabilistic
number theory in a unified manner. The main concepts will be presented
in parallel with the proof of three main theorems: (1) the Erdös-Kac
theorem and its variants concerning the number of prime divisors of
integers in various sequences; (2) the distribution of values of the
Riemann zeta function, including Selberg's central limit theorem for the
Riemann zeta function on the critical line; (3) functional limit
theorems for the paths of partial sums of families of exponential sums
such as Kloosterman sums.
LiteraturH. Iwaniec and E. Kowalski: "Analytic number theory", and additional
lecture notes will be prepared.
Voraussetzungen / BesonderesPrerequisites: Complex analysis, measure and integral; some probability theory is useful but the main concepts needed will be recalled.
Some knowledge of number theory is useful but the main results will be summarized.