401-3109-65L Probabilistic Number Theory
Semester | Herbstsemester 2015 |
Dozierende | E. Kowalski |
Periodizität | einmalige Veranstaltung |
Lehrsprache | Englisch |
Kurzbeschreibung | The 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 | |
Inhalt | The 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. |
Literatur | H. Iwaniec and E. Kowalski: "Analytic number theory", and additional lecture notes will be prepared. |
Voraussetzungen / Besonderes | Prerequisites: 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. |