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Viac informácií o knihe Diophantine Equations and Inequalities in Algebraic Number Fields

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• Obľúbené z iného súdka

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Anotácia knihy

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

Parametre knihy

Zaradenie knihy Knihy po anglicky Mathematics & science Mathematics Number theory

• Celý názov: Diophantine Equations and Inequalities in Algebraic Number Fields
• Autor: Yuan Wang
• Jazyk: Angličtina
• Väzba: Brožovaná
• Počet strán: 170
• EAN: 9783642634895
• ISBN: 9783642634895
• ID: 06616258
• Nakladateľ: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Hmotnosť: 341 g
• Rozmery: 242 × 170 × 11 mm
• Dátum vydania: 18. October 2012

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