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Author: Yu.I. Manin
Publisher: Elsevier
ISBN: 9780080963167
Category : Mathematics
Languages : en
Pages : 325
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Book Description
Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references. The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.
Author: Yu.I. Manin
Publisher: Elsevier
ISBN: 9780080963167
Category : Mathematics
Languages : en
Pages : 325
Get Book
Book Description
Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references. The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.
Author: Tim Browning
Publisher: Springer Nature
ISBN: 3030868729
Category : Mathematics
Languages : en
Pages : 175
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Book Description
The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Author: I︠U︡ I. Manin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Author: Samuel A. Hambleton
Publisher: Springer
ISBN: 3030014045
Category : Mathematics
Languages : en
Pages : 493
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Book Description
The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory. The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.
Author: Leonard Eugene Dickson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Author: James Joseph Sylvester
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097614
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Author: Arthur Cayley
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 642
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Book Description
Author: Alfred Edwin Howard Tutton
Publisher:
ISBN:
Category : Crystallography
Languages : en
Pages : 272
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Book Description
Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 3662080052
Category : Mathematics
Languages : en
Pages : 311
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Book Description
A unified survey of both the status quo and the continuing trends of various branches of number theory. Motivated by elementary problems, the authors present todays most significant results and methods. Topics covered include non-Abelian generalisations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. The book is rounded off with an overview of the major conjectures, most of which are based on analogies between functions and numbers, and on connections with other branches of mathematics such as analysis, representation theory, geometry and algebraic topology.
