{ "item_title" : "Diophantine Equations and Inequalities in Algebraic Number Fields", "item_author" : [" Yuan Wang "], "item_description" : "The circle method has its genesis in a paper of Hardy and Ramanujan (seeHardy 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 (seeHardy 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 Hilbert1] 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", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/3/64/263/489/3642634893_b.jpg", "price_data" : { "retail_price" : "54.99", "online_price" : "54.99", "our_price" : "54.99", "club_price" : "54.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

Overview

Customers Also Bought

Details