21 citations · 52 across the 30 of their papers we have counts for
8 papers · 1 filter
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-Existence of Some Nearly Perfect Sequences, Near Butson-Hadamard Matrices, and Near Conference Matrices
Arne Winterhof, Oğuz Yayla, Volker Ziegler
In this paper we study the non-existence problem of (nearly) perfect (almost) -ary sequences via their connection to (near) Butson-Hadamard (BH) matrices and (near) conference m…
A note on the number of -Diophantine quadruples
Florian Luca, Volker Ziegler
Let be an -tuple of positive, pairwise distinct, integers. If for all the prime divisors of come from the same fixed set , t…
On corner avoidance of -adic Halton sequences
Markus Hofer, Volker Ziegler
We consider the corner avoiding property of -dimensional -adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that t…
S-Diophantine quadruples with
László Szalay, Volker Ziegler
Let denote a set of primes and let be positive distinct integers. We call the -tuple an -Diophantine tuple if are $…
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,…
On Simultaneous Palindromes
Attila Bérczes, Volker Ziegler
A palindrome in base is an integer that remains the same when its digit expansion in base is reversed. Let and be given distinct integers . In this paper we…
On distinct unit generated fields that are totally complex
Daniel Dombek, Zuzana Masáková, Volker Ziegler
We consider the problem of characterizing all number fields such that all algebraic integers can be written as the sum of distinct units of . We extend a method due…