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Diophantine Approximations and Diophantine Equations
Wolfgang M. Schmidt
- 01 Aug 1991
349
TL;DR: Siegel's lemma and heights, Diophantine approximation, The thue equation, S-unit equations and hyperelliptic equations as discussed by the authors, S-Unit equations in more than two variables
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Abstract: Siegel's lemma and heights- Diophantine approximation- The thue equation- S-unit equations and hyperelliptic equations- Diophantine equations in more than two variables
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Citations
On Arithmetic Progressions in Recurrences -\\ A new characterization of the Fibonacci sequence
Ákos Pintér,Volker Ziegler +1 more
TL;DR: In this article, it was shown that the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions, and a criterion for general linear recurrences having infinitely many 3-term progressions is also given.
7
Heights and Determinants over Quaternion Algebras
TL;DR: In this article, a non-commutative analogue of the Cauchy-Binet formula for matrices over positive definite rational quaternion algebras is presented.
7
Almost fifth powers in arithmetic progression
TL;DR: In this article, the product of k consecutive terms of a primitive arithmetic progression is never a perfect fifth power when 3 ⩽ k⩽ 54 and the product is an almost fifth power.
7
Upper bounds for the number of solutions to quartic thue equations
TL;DR: This manuscript improves the results of author's earlier work with Okazaki by giving special treatments to forms with respect to their signature by using a logarithmic curve that allows to use the theory of linear forms inlogarithms.
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