Effective Results for Diophantine Problems Over Finitely Generated Domains
Author: Attila Bérczes
Publisher:
Published: 2016
Total Pages: 0
ISBN-13:
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Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
Published: 2022-04-28
Total Pages: 242
ISBN-13: 1009050036
DOWNLOAD EBOOKThis book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
Published: 2022-04-28
Total Pages: 241
ISBN-13: 1009005855
DOWNLOAD EBOOKProvides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.
Unit Equations in Diophantine Number Theory
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
Published: 2015-12-30
Total Pages: 381
ISBN-13: 1316432351
DOWNLOAD EBOOKDiophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.
Discriminant Equations in Diophantine Number Theory
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
Published: 2016-11-03
Total Pages: 477
ISBN-13: 1316727815
DOWNLOAD EBOOKDiscriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.
Number Theory – Diophantine Problems, Uniform Distribution and Applications
Author: Christian Elsholtz
Publisher: Springer
Published: 2017-05-26
Total Pages: 447
ISBN-13: 3319553577
DOWNLOAD EBOOKThis volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.
Discriminant Equations in Diophantine Number Theory
Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
Published: 2017
Total Pages: 477
ISBN-13: 1107097614
DOWNLOAD EBOOKThe first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
The Calabi Problem for Fano Threefolds
Author: Carolina Araujo
Publisher: Cambridge University Press
Published: 2023-06-30
Total Pages: 451
ISBN-13: 1009193392
DOWNLOAD EBOOKThis book determines whether the general element of each family of Fano threefolds is K-polystable, a major problem in mathematics.
Recent Developments in Algebraic Geometry
Author: Hamid Abban
Publisher: Cambridge University Press
Published: 2022-09-30
Total Pages: 368
ISBN-13: 1009190822
DOWNLOAD EBOOKWritten in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.
Reviews in Number Theory, 1984-96
Author:
Publisher: American Mathematical Society(RI)
Published: 1997
Total Pages: 1084
ISBN-13:
DOWNLOAD EBOOKThese six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews (MR) between 1984 and 1996. This is the third such set of volumes in number theory: the first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.
