R. Tichy

activity

20112026

most citedErgodic properties of β-adic Halton sequences

20 citations · 52 across the 37 of their papers we have counts for

collaborators

43 papers

math.NT2026

Distribution properties of generalized polynomials

Manfred G. Madritsch, Robert F. Tichy

A generalized polynomial is a function defined by an iteration of the operations addition, multiplication and the floor function. Equidistribution results of sequences given by gen…

math.FA2026

Lacunary Series, Nonlinear Functionals and Banach Space Structure

Istvan Berkes, Eduard Stefanescu, Robert Tichy

In a previous paper \cite{BT} we studied the asymptotic behavior of $∥ \sum_{k = 1}^{N} a_{k} X_{n_{k}} ∥_{p}$ for lacunary sequences $(X_{n_{k}})$ of random variables in $L_{p}$ and used the r…

math.NT2025

On Finite Pseudorandom Binary Sequences: Generalized polynomials

Manfred G. Madritsch, Robert F. Tichy

In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition…

math.FA2025

A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces

Istvan Berkes, Eduard Stefanescu, Robert Tichy

In this paper, we extend the Marcinkiewicz--Zygmund inequality to the setting of Orlicz and Lorentz spaces. Furthermore, we generalize a Kadec--Pełczyński-type result -- originally…

math.NT2023

On Finite Pseudorandom Binary Sequences: Functions from a Hardy field

Manfred G. Madritsch, Joël Rivat, Robert F. Tichy

We provide a construction of binary pseudorandom sequences based on Hardy fields $H$ as considered by Boshernitzan. In particular we give upper bounds for the well distri…

math.CO2023

A Local Limit Theorem for Integer Partitions into Small Powers

Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy

The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0 < α < 1$ were of recent int…

math.NT2023

Irreducibility properties of Carlitz' binomial coefficients for algebraic function fields

Robert Tichy, Daniel Windisch

We study the class of univariate polynomials $β_{k} (X)$ , introduced by Carlitz, with coefficients in the algebraic function field $F_{q} (t)$ over the finite field $F_{q}$ …

math.NT2023

Lacunary sequences in analysis, probability and number theory

Christoph Aistleitner, Istvan Berkes, Robert Tichy

In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe th…

math.NT2022★ 2 cited

On the Diophantine equation $U_{n} - b^{m} = c$

Sebastian Heintze, Robert F. Tichy, Ingrid Vukusic +1

Let $(U_{n})_{n \in N}$ be a fixed linear recurrence sequence defined over the integers (with some technical restrictions). We prove that there exist effectively computable c…

math.NT2022★ 5 cited

A Central Limit Theorem for Integer Partitions into Small Powers

Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy

The study of the well-known partition function $p (n)$ counting the number of solutions to $n = a_{1} + \dots + a_{ℓ}$ with integers $1 \leq a_{1} \leq \dots \leq a_{ℓ}$ has a…

math.NT2021★ 1 cited

On the Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences

Mahadi Ddamulira, Florian Luca, Robert Tichy

Let $r \geq 1$ be an integer and $U := {U_{n}}_{n \geq 0}$ be the Lucas sequence given by $U_{0} = 0, U_{1} = 1$ , and $U_{n + 2} = r U_{n + 1} + U_{n}$ for $n \geq 0$ . In this paper, we explain how to…

math.NT2020

On a variant of Pillai's problem with transcendental numbers

Robert Tichy, Ingrid Vukusic, Daodao Yang +1

In this paper, we study the asymptotic behaviour of the number of solutions $(m, n) \in N^{2}$ to the inequality $∣ α^{n} - β^{m} ∣ \leq x$ when $x$ tends to infinity. Here $α,…

math.NT2018★ 1 cited

Measurable Sequences

Milan Pasteka, Robert Tichy

The paper deals with real valued sequences and its distribution on real line.

math.PR2017

Lacunary series and stable distributions

I. Berkes, R. Tichy

By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the…

math.PR2017

On permutation-invariance of limit theorems

I. Berkes, R. Tichy

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only exp…

math.PR2017

Integral equations, quasi-Monte Carlo methods and risk modelling

Michael Preischl, Stefan Thonhauser, Robert F. Tichy

We survey a QMC approach to integral equations and develop some new applications to risk modeling. In particular, a rigorous error bound derived from Koksma-Hlawka type inequalitie…

math.CA2016

On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling

Gregory Derfel, Peter J. Grabner, Robert F. Tichy

We study the asymptotic behaviour of the solutions of a functional- differential equation with rescaling, the so-called pantograph equation. From this we derive asymptotic informat…

math.NT2016

Computable Absolutely Pisot Normal Numbers

Manfred G. Madritsch, Adrian-Maria Scheerer, Robert F. Tichy

We analyze the convergence order of an algorithm producing the digits of an absolutely normal number. Furthermore, we introduce a stronger concept of absolute normality by allowing…

math.NT2016

On Weyl products and uniform distribution modulo one

Christoph Aistleitner, Gerhard Larcher, Friedrich Pillichshammer +2

In the present paper we study the asymptotic behavior of trigonometric products of the form $\prod_{k = 1}^{N} 2 sin (π x_{k})$ for $N \to \infty$ , where the numbers $ω = (x_{k})_{k = 1}^{N}$ are…

math.MG2016

Constrained Triangulations, Volumes of Polytopes, and Unit Equations

Michael Kerber, Robert Tichy, Mario Weitzer

Given a polytope $P$ in $R^{d}$ and a subset $U$ of its vertices, is there a triangulation of $P$ using $d$ -simplices that all contain $U$ ? We answer thi…

math.NT2016

Multidimensional van der Corput sets and small fractional parts of polynomials

Manfred G. Madritsch, Robert F. Tichy

We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$ , in particular for sequences $ν (n) = ⌊ n^{c} ⌋ + n^{k}$ with $c > 1$ a non-integral r…

math.DS2016

Linear recursive odometers and beta-expansions

Maria Rita Iacò, Wolfgang Steiner, Robert F. Tichy

The aim of this paper is to study the connection between different properties related to $β$ -expansions. In particular, the relation between two conditions, both ensuring pure disc…

math.NT2016

On the regularity of primes in arithmetic progressions

Christian Elsholtz, Niclas Technau, Robert Tichy

We prove that for a positive integer $k$ the primes in certain kinds of intervals can not distribute too 'uniformly' among the reduced residue classes modulo $k$ . Hereby, we prove…

math.NT2016

Diophantine equations and the monodromy groups

Dijana Kreso, Robert F. Tichy

We study Diophantine equations of type f(x)=g(y), where both f and g have at least two distinct critical points and equal critical values at at most two distinct critical points. S…

Distribution properties of generalized polynomials

Lacunary Series, Nonlinear Functionals and Banach Space Structure

On Finite Pseudorandom Binary Sequences: Generalized polynomials

A Marcinkiewicz-Zygmund inequality and the Kadec Pełczynśki theorem in Orlicz spaces

On Finite Pseudorandom Binary Sequences: Functions from a Hardy field

A Local Limit Theorem for Integer Partitions into Small Powers

Irreducibility properties of Carlitz' binomial coefficients for algebraic function fields

Lacunary sequences in analysis, probability and number theory

On the Diophantine equation Un​−bm=c

A Central Limit Theorem for Integer Partitions into Small Powers

On the Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences

On a variant of Pillai's problem with transcendental numbers

Measurable Sequences

Lacunary series and stable distributions

On permutation-invariance of limit theorems

Integral equations, quasi-Monte Carlo methods and risk modelling

On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling

Computable Absolutely Pisot Normal Numbers

On Weyl products and uniform distribution modulo one

Constrained Triangulations, Volumes of Polytopes, and Unit Equations

Multidimensional van der Corput sets and small fractional parts of polynomials

Linear recursive odometers and beta-expansions

On the regularity of primes in arithmetic progressions

Diophantine equations and the monodromy groups

On the Diophantine equation $U_{n} - b^{m} = c$