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401-3117-66L  Introduction to the Circle Method

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


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