Diophantine Equations and Power Integral Bases: Theory and Algorithms, Gaбl Istvбn
Автор: W.M. Schmidt Название: Diophantine Approximation ISBN: 3540097627 ISBN-13(EAN): 9783540097624 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1970, at the University of Colorado, the author delivered a course of lectures on his famous generalization, relating to Roth`s theorem on rational approxi- mations to algebraic numbers. This volume is a version of the original mimeographed notes on the course.
Автор: Umberto Zannier Название: On Some Applications of Diophantine Approximations ISBN: 8876425195 ISBN-13(EAN): 9788876425196 Издательство: Springer Рейтинг: Цена: 3634.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel`s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel`s proof have appeared, but none seem to faithfully reproduce all features of the original one.
Описание: Introduction.- Negatively curved geometry.- Potentials, critical exponents and Gibbs cocycles.- Patterson-Sullivan and Bowen-Margulis measures with potential on CAT(-1) spaces.- Symbolic dynamics of geodesic flows on trees.- Random walks on weighted graphs of groups.- Skinning measures with potential on CAT(-1) spaces.- Explicit measure computations for simplicial trees and graphs of groups.- Rate of mixing for the geodesic flow.- Equidistribution of equidistant level sets to Gibbs measures.- Equidistribution of common perpendicular arcs.- Equidistribution and counting of common perpendiculars in quotient spaces.- Geometric applications.- Fields with discrete valuations.- Bruhat-Tits trees and modular groups.- Rational point equidistribution and counting in completed function fields.- Equidistribution and counting of quadratic irrational points in non-Archimedean local fields.- Counting and equidistribution of crossratios.- Counting and equidistribution of integral representations by quadratic norm forms.- A - A weak Gibbs measure is the unique equilibrium, by J. Buzzi.- List of Symbols.- Index.- Bibliography.
Автор: Istv?n Ga?l Название: Diophantine Equations and Power Integral Bases ISBN: 3030238644 ISBN-13(EAN): 9783030238643 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis.
Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied.
Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required.
Автор: Andreescu Titu Название: Quadratic Diophantine Equations ISBN: 1493938800 ISBN-13(EAN): 9781493938803 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book reveiws the last two decades of computational techniques and progress in the classical theory of quadratic diophantine equations. Presents important quadratic diophantine equations and applications, and includes excellent examples and open problems.
Автор: Vladimir G. Sprindzuk Название: Classical Diophantine Equations ISBN: 3540573593 ISBN-13(EAN): 9783540573593 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph provides a detailed discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to the obtaining of upper bounds for solutions to the eponymous classical diophantine equation.
Автор: Evertse Название: Unit Equations in Diophantine Number Theory ISBN: 1107097606 ISBN-13(EAN): 9781107097605 Издательство: Cambridge Academ Рейтинг: Цена: 10611.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Unit equations play a central role in Diophantine number theory. This book provides a comprehensive and up-to-date treatment of unit equations and their various applications. It brings together the most important results and gives an overview of the basic techniques, making it accessible to young researchers.
Описание: 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
Автор: Smart Nigel P. Название: The Algorithmic Resolution of Diophantine Equations ISBN: 0521646332 ISBN-13(EAN): 9780521646338 Издательство: Cambridge Academ Рейтинг: Цена: 9187.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A coherent account of the computational methods used to solve diophantine equations. Topics include local methods, sieving, descent arguments, the LLL algorithm, Baker`s theory of linear forms in logarithms, and problems associated with curves. Useful exercises and bibliography are included. Suitable for graduate students and research workers.
Автор: Evertse, Jan-hendrik (universiteit Leiden) Gyory, Kalman (debreceni Egyetem, Hungary) Название: Effective results and methods for diophantine equations over finitely generated domains ISBN: 1009005855 ISBN-13(EAN): 9781009005852 Издательство: Cambridge Academ Рейтинг: Цена: 8712.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a comprehensive guide to Diophantine equations over finitely generated domains, with a focus on proving effective finiteness results. No specialized knowledge is required, enabling graduate students and experts alike to learn the necessary techniques and apply them in their own research.
Автор: Evertse Название: Discriminant Equations in Diophantine Number Theory ISBN: 1107097614 ISBN-13(EAN): 9781107097612 Издательство: Cambridge Academ Рейтинг: Цена: 23285.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discriminant equations are an important class of Diophantine equations. This book provides the first comprehensive account of discriminant equations and their applications, building on the authors` earlier volume, Unit Equations in Diophantine Number Theory. Background material makes the book accessible to experts and young researchers alike.
Автор: Corvaja Pietro Название: Applications of Diophantine Approximation to Integral Points ISBN: 1108424945 ISBN-13(EAN): 9781108424943 Издательство: Cambridge Academ Рейтинг: Цена: 18216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to Diophantine approximation and Diophantine equations, with applications to related topics, pays special regard to Schmidt`s subspace theorem. It contains a number of results, some never before published in book form, and some new. The authors introduce various techniques and open questions to guide future research.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru
