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9781107097605

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'The book is well written and is certain to be of use to experts and graduate students alike. Every chapter is prefaced with a nice introduction and summary, putting the material in perspective and surveying the proof techniques. The book also features an extensive bibliography and an easy-to-use glossary and index.' Lenny Fukshansky, MathSciNet 'Understanding the book requires only basic knowledge in algebra (groups, commutative rings, fields, Galois theory and elementary algebraic number theory). In particular the concepts of height, places and valuations play an important role. ... In addition to providing a survey, the authors improve both formulations and proofs of various important existing results in the literature, making their book a valuable asset for researchers in this area. ... I thank them for their fast and clear answers.' Pieter Moree, Nieuw Archief voor Wiskunde 'The book is well written and is certain to be of use to experts and graduate students alike. Every chapter is prefaced with a nice introduction and summary, putting the material in perspective and surveying the proof techniques. The book also features an extensive bibliography and an easy-to-use glossary and index.' Lenny Fukshansky, MathSciNet 'Understanding the book requires only basic knowledge in algebra (groups, commutative rings, fields, Galois theory and elementary algebraic number theory). In particular the concepts of height, places and valuations play an important role. ... In addition to providing a survey, the authors improve both formulations and proofs of various important existing results in the literature, making their book a valuable asset for researchers in this area. ... I thank them for their fast and clear answers.' Pieter Moree, Nieuw Archief voor Wiskunde

'The book is well written and is certain to be of use to experts and graduate students alike. Every chapter is prefaced with a nice introduction and summary, putting the material in perspective and surveying the proof techniques. The book also features an extensive bibliography and an easy-to-use glossary and index.' Lenny Fukshansky, MathSciNet

'The book is well written and is certain to be of use to experts and graduate students alike. Every chapter is prefaced with a nice introduction and summary, putting the material in perspective and surveying the proof techniques. The book also features an extensive bibliography and an easy-to-use glossary and index.' Lenny Fukshansky, MathSciNet 'Understanding the book requires only basic knowledge in algebra (groups, commutative rings, fields, Galois theory and elementary algebraic number theory). In particular the concepts of height, places and valuations play an important role. ... In addition to providing a survey, the authors improve both formulations and proofs of various important existing results in the literature, making their book a valuable asset for researchers in this area. ... I thank them for their fast and clear answers.' Pieter Moree, Nieuw Archief voor Wiskunde

Author Information

Jan-Hendrik Evertse is Assistant Professor 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. He has written more than 75 research papers and co-authored one book with Bas Edixhoven entitled Diophantine Approximation and Abelian Varieties (2003). 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, decomposable form equations, and their various applications. His results have been published in one book and 160 research papers. 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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