On the number of pairs of binary forms with given degree and given resultant

Bérczes, Attila; Evertse, Jan–Hendrik; Győry, Kálmán

doi:10.4064/aa128-1-2

Cited by 2 publications

(1 citation statement)

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“…Let f ∈ Z[X, Y ] be an irreducible form of degree at least 3 and m ∈ Z\{0}. The equation [71]: results for finitely generated domains. Since it is known that a single Thue equation has only finitely many solutions and these solutions can, at least in principle, be calculated, the research focused on solving families of Thue equations…”

Section: Some Of the Most Important Joint Research Topics And Resultsmentioning

confidence: 99%

30 years of collaboration

Fuchs

Hajdu

2016

Period Math Hung

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Abstract. We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem), which will be presented in turn.

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Section: Some Of the Most Important Joint Research Topics And Resultsmentioning

confidence: 99%

30 years of collaboration

Fuchs

Hajdu

2016

Period Math Hung

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Unit Equations in Diophantine Number Theory

Evertse

Győry

2015

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Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

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On the number of pairs of binary forms with given degree and given resultant

Cited by 2 publications

References 9 publications

30 years of collaboration

30 years of collaboration

Unit Equations in Diophantine Number Theory

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