Applications of Diophantine Approximation to Integral Points and Transcendence

  title={Applications of Diophantine Approximation to Integral Points and Transcendence},
  author={Pietro Corvaja and Umberto Zannier},
Diophantine approximation may be roughly described as the branch of number theory concerned with approximations by rational numbers; or rather, this constituted the original motivation. That such questions have attracted continued attention is undoubtedly substantially due to their relevance for another, more ancient, topic: the theory of Diophantine equations, namely those whose solutions have to be found in integers or rationals, possibly in a finite extension of Q. The connections between… 


  • Mathematics
  • 2020
Diophantine Geometry aims to describe the sets of rational and/or integral points on a variety. More precisely one would like geometric conditions on a variety X that determine the distribution of

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Let K be a number field. It is well known that the set of recurrencesequences with entries in K is closed under component-wise operations, and so it can be equipped with a ring structure. We try to

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In the present paper we solve, in particular, the function field version of a special case of Vojta’s conjecture for integral points, namely for the variety obtained by removing a conic and two lines

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In 1929 Siegel proved a celebrated theorem on finiteness for integral solutions of certain diophantine equations. This theorem applies to systems of polynomial equations which either (a) describe an

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