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Effective Results and Methods for Diophantine Equations over Finitely Generated Domains by Jan-Hendrik Evertse

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

by Jan-Hendrik Evertse , Kálmán Győry
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Book cover type: Paperback
  • ISBN13: 9781009005852
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 240
  • Original Price: GBP 57.99
  • Language: English
  • Edition: N/A
  • Item Weight: 377 grams
  • BISAC Subject(s): Number Theory

This 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.

Evertse, Jan-Hendrik: - 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).

Győry, Kálmán: - 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).

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