On the Lenstra constant associated to the Rosen continued fractions
Hitoshi Nakada (2010)
Journal of the European Mathematical Society
Similarity:
Hitoshi Nakada (2010)
Journal of the European Mathematical Society
Similarity:
Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt (2013)
Journal of the European Mathematical Society
Similarity:
We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.
Thomas A. Schmidt, Mark Sheingorn (1995)
Compositio Mathematica
Similarity:
Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
Similarity:
Takao Komatsu (2003)
Acta Arithmetica
Similarity:
S. G. Dani (2015)
Acta Arithmetica
Similarity:
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...
James Mc Laughlin (2008)
Acta Arithmetica
Similarity:
Boris Adamczewski (2010)
Acta Arithmetica
Similarity:
Cornelis Kraaikamp, Thomas A. Schmidt, Ionica Smeets (2007)
Journal de Théorie des Nombres de Bordeaux
Similarity:
In the 1990s, J.C. Tong gave a sharp upper bound on the minimum of consecutive approximation constants for the nearest integer continued fractions. We generalize this to the case of approximation by Rosen continued fraction expansions. The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best possible upper bound for the minimum in appropriate consecutive blocks of...
Douglas Bowman, Alexandru Zaharescu (2012)
Acta Arithmetica
Similarity:
J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
Similarity:
Sergio Albeverio, Oleksandr Baranovskyi, Mykola Pratsiovytyi, Grygoriy Torbin (2007)
Acta Arithmetica
Similarity:
Anton Lukyanenko, Joseph Vandehey (2015)
Acta Arithmetica
Similarity:
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
Similarity: