Modular embeddings for some non-arithmetic Fuchsian groups
Monotone subsequences in the sequence of fractional parts of multiples of an irrational.
More on inhomogeneous diophantine approximation
For an irrational real number and real number we consider the inhomogeneous approximation constantvia the semi-regular negative continued fraction expansion of
Morphic and automatic words: maximal blocks and Diophantine approximation
Motzkin paths and powers of continued fractions.
Multi-continued fraction algorithm on multi-formal Laurent series
Multidimensional Euclidean algorithms.
Multidimensional Gauss reduction theory for conjugacy classes of
In this paper we describe the set of conjugacy classes in the group . We expand geometric Gauss Reduction Theory that solves the problem for to the multidimensional case, where -reduced Hessenberg matrices play the role of reduced matrices. Further we find complete invariants of conjugacy classes in in terms of multidimensional Klein-Voronoi continued fractions.
Multiplication par un entier d'une fraction continue périodique
Multiplication par un entier d'une fraction continue périodique
Multiplicative dependence in number fields
Multiplicative relations on binary recurrences
Given a binary recurrence , we consider the Diophantine equation with nonnegative integer unknowns , where for 1 ≤ i < j ≤ L, , and K is a fixed parameter. We show that the above equation has only finitely many solutions and the largest one can be explicitly bounded. We demonstrate the strength of our method by completely solving a particular Diophantine equation of the above form.
Multiplicative zero-one laws and metric number theory
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher...
Multiplicatively dependent triples of Tribonacci numbers
We consider the Tribonacci sequence given by T₀ = 0, T₁ = T₂ = 1 and for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.
Multiplicity estimate for solutions of extended Ramanujan’s system
We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).
Multiplicity estimates and the product theorem
Multiplicity estimates for analytic functions. I.
Multiplicity estimates for certain pairs of functions involving Drinfeld modular forms
Multisoliton formula for completely integrable two-dimensional systems
Neuer Beweis eines Minkowskischen Satzes.