Diophantine Equations and Inequalities in Algebraic Number Fields is popular PDF and ePub book, written by Yuan Wang in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Diophantine Equations and Inequalities in Algebraic Number Fields can be Read Online from any device for your convenience.
Diophantine Equations and Inequalities in Algebraic Number Fields Book PDF Summary
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
Detail Book of Diophantine Equations and Inequalities in Algebraic Number Fields PDF
- Author : Yuan Wang
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642581717
- Genre : Mathematics
- Total Page : 185 pages
- Language : English
- PDF File Size : 16,5 Mb
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