401-3109-65L  Probabilistic Number Theory

SemesterSpring Semester 2021
LecturersE. Kowalski
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3109-65 GProbabilistic Number Theory4 hrs
Mon10:15-12:00ML F 39 »
Thu14:15-16:00HG D 5.2 »
E. Kowalski

Catalogue data

AbstractThe course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums.
ObjectiveThe goal of the course is to present some results of probabilistic number theory in a unified manner.
ContentThe main concepts will be presented in parallel with the proof of a few main theorems:
(1) the Erdős-Wintner and Erdős-Kac theorems concerning the distribution of values of arithmetic functions;
(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) the Chebychev bias for primes in arithmetic progressions;
(4) functional limit theorems for the paths of partial sums of families of exponential sums.
Lecture notesThe lecture notes for the class are available at

Link
Prerequisites / NoticePrerequisites: Complex analysis, measure and integral, and at least the basic language of probability theory (the main concepts, such as convergence in law, will be recalled).
Some knowledge of number theory is useful but the main results will also be summarized.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits8 credits
ExaminersE. Kowalski
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
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Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics BachelorSelection: Algebra, Number Thy, Topology, Discrete Mathematics, LogicWInformation
Mathematics MasterSelection: Algebra, Number Thy, Topology, Discrete Mathematics, LogicWInformation