Constructions of plane curves with many points
Constructions of smooth and analytic cocycles over irrational circle rotations
We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk,...
Constructive and non-constructive methods of proofs of irrationality and transcendency and algebraic independence of periods of abelian varieties
Construire un noyau de la fonctorialité ? Le cas de l’induction automorphe sans ramification de GL à GL
Le but de cet article est de présenter une nouvelle méthode purement adélique pour réaliser le principe de fonctorialité de Langlands dans le cas de l’induction automorphe sans ramification de GL à GL sur les corps de fonctions. On construit sur le produit des groupes adéliques GL et GL un noyau de la fonctorialité. C’est une version “en famille” et locale de la construction par les modèles de Whittaker globaux, utilisée classiquement dans les “théorèmes réciproques” de Weil et Piatetski-Shapiro....
Continuants with Bounded Digits - III.
Continued fraction expansions for complex numbers-a general approach
We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values...
Continued fractions and Catalan problems.
Continued fractions and class number two.
Continued fractions and density results for Dedekind sums.
Continued fractions and the Gauss map.
Continued fractions and transcendental numbers
The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].
Continued fractions and transformations of integer sequences.
Continued fractions, Fibonacci numbers, and some classes of irrational numbers.
Continued fractions for finite sums
Continued fractions for some algebraic numbers.
Continued Fractions for Some Alternating Series.
Continued fractions, multidimensional diophantine approximations and applications
This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Continued fractions of Laurent series with partial quotients from a given set
Continued fractions of period five and real quadratic fields of class number one
Continued Fractions of Transcendental Numbers