Related papers: Rational numbers represented by sign-variable Cant…
We establish various new results on a problem proposed by K. Mahler in 1984 concerning rational approximation to fractal sets by rational numbers inside and outside the set in question, respectively. Some of them provide a natural…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.
The aim of these notes is to give a introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves which are the higher dimensional analogs of rational curves…
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.
We show conditions on $k$ such that any number $x$ in the interval $[0, k/2]$ can be represented in the form $x_1^{a_1} x_2^{a_2} + x_3^{a_3} x_4^{a_4} + \cdots + x_{k-1}^{a_{k-1}} x_k^{a_k}$, where the exponents $a_{2i-1}$ and $a_{2i}$ are…
This paper is an investigation into Cantor works about representing a function with trigonometric series, and his proofs about its uniqueness. These works are important, because they cause invention of point-set topology, and foundation of…
It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra…
We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers…
The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic…
We give description of rational solutions of polynomial-equations.
We give new arguments for sums and products of sufficient numbers of arbitrary central Cantor sets to produce large open intervals. We further discuss the same question for $C^1$ images of such central Cantor sets. This gives another…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
These expository notes discuss the arithmetic of rationally connected varieties. Detailed proofs of theorems of Koll\'ar, of Koll\'ar and Szab\'o and of Esnault about rationally connected varieties over finite fields and local fields are…
This is an expository paper on rationally connected varieties. The aim is to provide an introduction to the subject, as well as to discuss a recent result by T. Graber, J. Harris and J. Starr. The paper is based on the talk I gave at the…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.
We show that the possible Cantor-Bendixson ranks of countable SFTs are exactly the finite ordinals and ordinals of the form $\lambda + 3$, where $\lambda$ is a computable ordinal. This result was claimed by the author in his PhD…