5 citations · 20 across the 19 of their papers we have counts for
22 papers
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…
Waring's problem for pseudo-polynomials
Manfred G. Madritsch
Waring's problem has a long history in additive number theory. In its original form it deals with the representability of every positive integer as sum of -th powers with intege…
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…
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 as considered by Boshernitzan. In particular we give upper bounds for the well distri…
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 were of recent int…
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 counting the number of solutions to with integers has a…
The level of distribution of the sum-of-digits function of linear recurrence number systems
Manfred G. Madritsch, Jörg M. Thuswaldner
Let be a strictly increasing linear recurrent sequence of integers with having characteristic polynomial . It is we…
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…
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 , in particular for sequences with a non-integral r…
Romanov's Theorem in Number Fields
Manfred G. Madritsch, Stefan Planitzer
Romanov proved that a positive proportion of the integers have a representation as a sum of a prime and a power of an arbitrary fixed positive integer. Rieger proved the analogous…
Hausdorff dimension of particularly non-normal numbers in dynamical systems fulfilling the specification property
Manfred G. Madritsch, Izabela Petrykiewicz
In this paper, we consider non-normal numbers occurring in dynamical systems fulfilling the specification property. It has been shown that in this case the set of non-normal number…
Dynamical systems and uniform distribution of sequences
M. G. Madritsch, R. F. Tichy
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational asp…
Construction of normal numbers via pseudo-polynomial prime sequences
Manfred G. Madritsch
In the present paper we construct normal numbers in base by concatenating -ary expansions of pseudo polynomials evaluated at the primes. This extends a recent result by Tich…
Forms of differing degrees over number fields
Christopher Frei, Manfred Madritsch
Consider a system of polynomials in many variables over the ring of integers of a number field . We prove an asymptotic formula for the number of integral zeros of this system i…
On multiplicatively independent bases in cyclotomic number fields
Manfred G. Madritsch, Volker Ziegler
Recently the authors showed that the algebraic integers of the form are bases of a canonical number system of provided , where denote…
Non-normal numbers with respect to infinite Markov partitions
Manfred Madritsch
In the present paper we investigate two special types of non-normal numbers. On the one hand we call a number extremely non-normal if the set of accumulation points of its frequenc…
Non-normal numbers in dynamical systems fulfilling the specification property
Manfred G. Madritsch, Izabela Petrykiewicz
In the present paper we want to focus on this dichotomy of the non-normal numbers -- on the one hand they are a set of measure zero and on the other hand they are residual -- for d…
An infinite family of multiplicatively independent bases of number systems in cyclotomic number fields
Manfred Madritsch, Volker Ziegler
Let be a -th primitive root of unity, an integer and the -th cyclotomic polynomial. In this paper we show that the pair $(-m+ζ_k,…
Construction of normal numbers via generalized prime power sequences
Manfred G. Madritsch, Robert F. Tichy
In the present paper the authors construct normal numbers in base by concatenating -adic expansions of prime powers with and .
Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k
Vitaly Bergelson, Grigori Kolesnik, Manfred Madritsch +2
We establish new results on sets of recurrence and van der Corput sets in Z^k which refine and unify some of the previous results obtained by Sarkozy, Furstenberg, Kamae and Mendes…
Construction of μ-normal sequences
Manfred G. Madritsch, Bill Mance
In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the…
Asymptotic normality of additive functions on polynomial sequences in canonical number systems
Manfred G. Madritsch, Attila PethHö
The objective of this paper is the study of functions which only act on the digits of an expansion. In particular, we are interested in the asymptotic distribution of the values of…