7 papers
Transcendence of continued fractions over function fields and a quantitative version of Uchiyama's theorem
Federico Accossato, Nadir Murru, Giuliano Romeo +1
Given a field , let be the field of formal power series. Continued fractions in can be defined by analogy with classical real continued fractions and…
Transcendence of -adic continued fractions and a quantitative -adic Roth theorem
Anne Kalitzin, Nadir Murru
In this paper, we improve some transcendence results for --adic continued fractions. In particular, we prove that palindromic and quasi--periodic --adic continued fractions c…
On the finiteness of -adic continued fractions for number fields
Laura Capuano, Nadir Murru, Lea Terracini
For a prime ideal of the ring of integers of a number field , we give a general definition of -adic continued fraction, which also includes classica…
On the arithmetic of multidimensional continued fractions
Piotr Miska, Nadir Murru, Giuliano Romeo
The problem of developing an arithmetic for continued fractions (in order to perform, e.g., sums and products) does not have a straightforward solution and has been addressed by se…
Transcendence criteria for multidimensional continued fractions
Federico Accossato, Nadir Murru, Giuliano Romeo
Classical results on Diophantine approximation, such as Roth's theorem, provide the most effective techniques for proving the transcendence of special kinds of continued fractions.…
Heights and transcendence of --adic continued fractions
Ignazio Longhi, Nadir Murru, Francesco Maria Saettone
Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous $…