Diophantine Equations Over Function Fields PDF Download
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Author: R. C. Mason
Publisher: Cambridge University Press
ISBN: 9780521269834
Category : Mathematics
Languages : en
Pages : 142
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Book Description
A self-contained account of a new approach to the subject.
Author: R. C. Mason
Publisher: Cambridge University Press
ISBN: 9780521269834
Category : Mathematics
Languages : en
Pages : 142
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Book Description
A self-contained account of a new approach to the subject.
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1009005855
Category : Mathematics
Languages : en
Pages : 241
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Book Description
Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.
Author: R. C. Mason
Publisher:
ISBN: 9781107093447
Category : Algebraic fields
Languages : en
Pages : 136
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Book Description
A self-contained account of a new approach to the subject.
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097606
Category : Mathematics
Languages : en
Pages : 381
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Book Description
A comprehensive, graduate-level treatment of unit equations and their various applications.
Author: Dana Schlomiuk
Publisher: American Mathematical Soc.
ISBN: 9780821869857
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.
Author:
Publisher: World Scientific
ISBN: 9789810224981
Category : Mathematics
Languages : en
Pages : 616
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Book Description
The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk ?Mathematics as Metaphor? summarises the author's view on mathematics as an outgrowth of natural language.
Author: Michael Rosen
Publisher: Springer Science & Business Media
ISBN: 1475760469
Category : Mathematics
Languages : en
Pages : 355
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Book Description
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
Author: István Gaál
Publisher: Springer Nature
ISBN: 3030238652
Category : Mathematics
Languages : en
Pages : 335
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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 9780521335454
Category : Mathematics
Languages : en
Pages : 456
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Book Description
This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.
Author: William Cherry
Publisher: American Mathematical Soc.
ISBN: 0821829807
Category : Mathematics
Languages : en
Pages : 146
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Book Description
This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point andgeneralizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the $abc$-conjecture, and Shiffman's conjecture.L. Keen and J. Kotus explore the dynamics of the family of $f \lambda(z)=\lambda\tan(z)$ and show that it has much in common with the dynamics of the familiar quadratic family $f c(z)=z2+c$. R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions. The bookis intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.
