Diophantine Equations and Inequalities in Algebraic Number Fields (Paperback, Softcover reprint of the original 1st ed. 1991)

The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep- resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum", Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad- ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s( k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Release date:	March 2013
First published:	1991
Authors:	Yuan Wang
Dimensions:	242 x 170 x 10mm (L x W x T)
Format:	Paperback
Pages:	170
Edition:	Softcover reprint of the original 1st ed. 1991
ISBN-13:	978-3-642-63489-5
Categories:	Books > Science & Mathematics > Mathematics > Number theory > General Promotions
LSN:	3-642-63489-3
Barcode:	9783642634895

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