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Effective results and methods for diophantine equations over finitely generated domains /

"This book is devoted to Diophantine equations where the solutions are taken from an integral domain of characteristic 0 that is finitely generated over Z, that is a domain of the shape Z[z1; : : : ; zr] with quotient field of characteristic 0, where the generators z1; : : : ; zr may be algebra...

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Bibliographic Details
Main Authors: Evertse, J. H.
Group Author: Györy, Kálmán
Published: Cambridge University Press,
Publisher Address: Cambridge, United Kingdom :
Publication Dates: 2022.
Literature type: Book
Language: English
Series: London Mathematical Society lecture note series ; 475
Subjects:
Diophantine equations.
Diophantine analysis.
Number theory.
Summary: "This book is devoted to Diophantine equations where the solutions are taken from an integral domain of characteristic 0 that is finitely generated over Z, that is a domain of the shape Z[z1; : : : ; zr] with quotient field of characteristic 0, where the generators z1; : : : ; zr may be algebraic or transcendental over Q. For instance, the ring of integers and the rings of S-integers of a number field are finitely generated domains where all generators are algebraic. Our aim is to prove effective finiteness results for certain classes of Diophantine equations, i.e., results that not only show that the equations from the said classes have only finitely many solutions, but whose proofs provide methods to determine the solutions in principle"--
Carrier Form: xxiv, 216 pages ; 23 cm.
Bibliography: Includes bibliographical references (pages 206-213) and index.
ISBN: 9781009005852
1009005855
Index Number: QA242
CLC: O156.7
Call Number: O156.7/E935-2
Contents: Ineffective results for Diophantine equations over finitely generated domains -- Effective results for Diophantine equations over finitely generated domains: the statements -- A brief explanation of our effective methods over finitely generated domains -- Effective results over number fields -- Effective results over function fields -- Tools from effective commutative algebra -- The effective specialization method -- Degree-height estimates -- Proofs of the results from Sections 2.2-2.5-use of specializations -- Proofs of the results from Sections 2.6-2.8-reduction to unit equations.

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