{"product_id":"diophantine-equations-and-inequalities-in-algebraic-number-fields-von-yuan-wang","title":"Diophantine Equations and Inequalities in Algebraic Number Fields","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\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642634895\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642634895","offer_id":39444946321501,"sku":"9783642634895","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/78c9e2a9-c0ad-4e25-827d-fe90e731de9b.jpg?v=1772085586","url":"https:\/\/shop.autorenwelt.de\/products\/diophantine-equations-and-inequalities-in-algebraic-number-fields-von-yuan-wang","provider":"Autorenwelt Shop","version":"1.0","type":"link"}