A remark on trigonometric sums
A Result from Diophantine Approximation which has Applications in Economics.
A rigidity phenomenon for the Hardy-Littlewood maximal function
The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as those nonconstant...
A Schinzel theorem on continued fractions in function fields
A Sequence Has Almost Nowhere Small Discrepancy.
A sharpening of the bounds for linear forms in logarithms
A sharpening of the bounds for linear forms in logarithms II
A sharpening of the bounds for linear forms in logarithms III
A Six Exponentials Theorem in Finite Characteristic.
A survey of results on density modulo of double sequences containing algebraic numbers
In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.
A Symbolic Dynamics for Geodesics on Punctured Riemann Surfaces.
A theorem on irrationality of infinite series and applications
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields.
A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties
A Lagrange Theorem in dimension 2 is proved in this paper, for a particular two dimensional continued fraction algorithm, with a very natural geometrical definition. Dirichlet type properties for the convergence of this algorithm are also proved. These properties proceed from a geometrical quality of the algorithm. The links between all these properties are studied. In relation with this algorithm, some references are given to the works of various authors, in the domain of multidimensional continued...
A Vanishing Theorem for Power Series.
About some inequalities concerning the fractional part.
Abschätzung der Periodenlänge einer verallgemeinerten Kettenbruchentwicklung.
Accélération de la convergence de certaines récurrences linéaires
Accumulation Points of the Lagrange and Markov Spectra.