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401-3117-66L  Introduction to the Circle Method

SemesterAutumn Semester 2016
LecturersE. Kowalski
Periodicitynon-recurring course
Language of instructionEnglish



Catalogue data

AbstractThe circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large.
Objective
ContentThe circle method, invented by Hardy and Ramanujan and developped by Hardy and
Littlewood and Kloosterman, is one of the most versatile methods currently available
to determine the asymptotic behavior of the number of integral solutions to
polynomial equations, when the number of solutions is sufficiently large.

The lecture will present an introduction to this method. In particular, it will
present the solution of Waring's Problem concerning the representability of integers
as sums of a bounded numbers of (fixed) powers of integers.
LiteratureH. Davenport, "Analytic methods for Diophantine equations and Diophatine
inequalities", Cambridge

H. Iwaniec and E. Kowalski, "Analytic number theory", chapter 20; AMS

R. Vaughan, "The Hardy-Littlewood method", Cambridge

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 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

No public learning materials available.
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-3117-66 VIntroduction to the Circle Method2 hrs
Thu13-15HG G 26.3 »
E. Kowalski
401-3117-66 UIntroduction to the Circle Method
NOTICE: on November 25, 2016 the exercises take place in HG F 26.1
1 hrs
Fri08-09HG F 3 »
25.11.08-09HG F 26.1 »
E. Kowalski

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics BachelorSelection: Algebra, Topology, Discrete Mathematics, LogicWInformation
Mathematics MasterSelection: Algebra, Topology, Discrete Mathematics, LogicWInformation