A New Infinite Product Representation for Real Numbers.
A new irrationality measure for ζ(3)
A new lower bound for
We prove that, for all integers exceeding some effectively computable number , the distance from to the nearest integer is greater than .
A non-standard metric in the group of reals
A note on a paper of Franklin
A note on a paper of Oppenheim and Šalát concerning series of Cantor type
A note on counting cuspidal excursions.
A note on Diophantine approximation.
A note on elliptic functions and approximation by algebraic numbers of bounded degree
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on irregularities in distribution of sequences of integers
A note on linear recurrent Mahler numbers.
A note on simultaneous Diophantine approximation in positive characteristic
A note on the diophantine equation
In this note we prove that the equation , , has only finitely many positive integer solutions . Moreover, all solutions satisfy , and .
A note on the diophantine equation
A note on the equation
A note on the Hausdorff-Besicovitch dimension of systems of linear forms
A note on the lonely runner conjecture.
A note on the transcendence of infinite products
The paper deals with several criteria for the transcendence of infinite products of the form where is a positive algebraic number having a conjugate such that , and are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès France, Acta...
A note on the weighted Khintchine-Groshev Theorem
Let denote the set of –approximable points in . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of and . It can not be removed for as Duffin–Schaeffer provided the counter example. We deal with the only remaining case and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem.