Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

Jan-Hendrik Evertse

ISBN 10: 1009005855 / ISBN 13: 9781009005852

Editore: Cambridge University Press Apr 2022, 2022

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Neuware - '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'--.

Codice articolo 9781009005852

Dati bibliografici

• Titolo: Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
• Editore: Cambridge University Press Apr 2022
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 1009005855
• ISBN 13: 9781009005852
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.

Informazioni sugli autori

Jan-Hendrik Evertse is Associate Professor in Number Theory at Leiden University in the Netherlands. He co-edited the lecture notes in mathematics Diophantine Approximation and Abelian Varieties (1993) with Bas Edixhoven, and co-authored two books with Kálmán Győry: Unit Equations in Diophantine Number Theory (Cambridge, 2016) and Discriminant Equations in Diophantine Number Theory (Cambridge, 2016).

Kálmán Győry is Professor Emeritus at the University of Debrecen, Hungary and a member of the Hungarian Academy of Sciences. Győry is the founder and leader of the Number Theory Research Group in Debrecen. Together with Jan-Hendrik Evertse he has written two books: Unit Equations in Diophantine Number Theory (Cambridge, 2016) and Discriminant Equations in Diophantine Number Theory (Cambridge, 2016).