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Jan-Hendrik Evertse, Kálmán Győry - Discriminant Equations in Diophantine Number Theory, Inbunden

Inbunden, Engelska, 2016

Del 32 i serien New Mathematical Monographs

Discriminant Equations in Diophantine Number Theory

Av Jan-Hendrik Evertse, Kálmán Győry

3209 kr

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Beskrivning
Discriminant 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.
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Jan-Hendrik Evertse works in the Mathematical Institute at Leiden University. His research concentrates on Diophantine approximation and applications to Diophantine problems. In this area he has obtained some influential results, in particular on estimates for the numbers of solutions of Diophantine equations and inequalities. Kálmán Győry is Professor Emeritus at the University of Debrecen, a member of the Hungarian Academy of Sciences and a well-known researcher in Diophantine number theory. Over his career he has obtained several significant and pioneering results, among others on unit equations and decomposable form equations, and their various applications. Győry is also the founder and leader of the Number Theory Research Group in Debrecen, which consists of his former students and their descendants.

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'… the book is very interesting and well written. It contains the motivational material necessary for those entering in the field of discriminant equations and succeeds to bring the reader to the forefront of research. Graduates and researchers in the field of number theory will find it a very valuable resource.' Dimitros Poulakis, Zentralblatt MATH

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