225 research outputs found
Extremal families of cubic Thue equations
We exactly determine the integral solutions to a previously untreated
infinite family of cubic Thue equations of the form with at least
such solutions. Our approach combines elementary arguments, with lower
bounds for linear forms in logarithms and lattice-basis reduction
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-HĂŒbner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro PezzĂ©, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
30 years of collaboration
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 RĂ©nyi and ErdĆs (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). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in GyĆr (Hungary)
On a parametric family of Thue inequalities over function fields
In this paper we completely solve a family of Thue inequalities defined over the field of functions , namely deg (X4â4cX3Y+(6c+2)X2Y2+4cXY3+Y4) †deg c, where the solutions x,y come from the ring and the parameter is some non-constant polynomia
Bounded Height in Pencils of Finitely Generated Subgroups
We prove height bounds concerning intersections of finitely generated
subgroups in a torus with algebraic subvarieties, all varying in a pencil. This
vastly extends the previously treated constant case and involves entirely
different, and more delicate, techniques
Continued fractions and transcendental numbers
It is widely believed that the continued fraction expansion of every
irrational algebraic number either is eventually periodic (and we know
that this is the case if and only if is a quadratic irrational), or it
contains arbitrarily large partial quotients. Apparently, this question was
first considered by Khintchine. A preliminary step towards its resolution
consists in providing explicit examples of transcendental continued fractions.
The main purpose of the present work is to present new families of
transcendental continued fractions with bounded partial quotients. Our results
are derived thanks to new combinatorial transcendence criteria recently
obtained by Adamczewski and Bugeaud
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