{"product_id":"9783642634895","title":"Diophantine Equations and Inequalities in Algebraic Number Fields (Reprint)","description":"\u003cp\u003eThe 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\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":42574965080139,"sku":"00000_00000_00000_00000","price":1960.57,"currency_code":"THB","in_stock":true}],"url":"https:\/\/kinokuniya.co.th\/th\/products\/9783642634895","provider":"Books Kinokuniya Thailand","version":"1.0","type":"link"}