A combinatorial inequality. (Eine kombinatorische Ungleichung.)
Kernels and Grundy functions on trees. (Kerne und Grundyfunktionen auf Bäumen.)
The height of -binary search trees.
The component distribution of saturated subgraphs of families of trees. (Die Komponentenverteilung von gesättigten Teilgraphen in Baumfamilien.)
The width of Galton-Watson trees conditioned by the size.
Zwei metrische Verebungssätze in der Theorie der Gleichverteilung.
The joint distribution of q-additive functions
Irregularities of continuous distributions
This paper deals with a continuous analogon to irregularities of point distributions. If a continuous fonction where is a compact body, is interpreted as a particle’s movement in time, then the discrepancy measures the difference between the particle’s stay in a proper subset and the volume of the subset. The essential part of this paper is to give lower bounds for the discrepancy in terms of the arc length of , . Furthermore it is shown that these estimates are the best possible despite of...
Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series.
The distribution of the sum-of-digits function
By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.
The Zeckendorf expansion of polynomial sequences
In the first part of the paper we prove that the Zeckendorf sum-of-digits function and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the -ary expansions of integers are asymptotically independent.
Relations between polynomial roots
Relations between polynomial roots
The joint distribution of -additive functions on polynomials over finite fields
Let be a finite field and a polynomial of positive degree. A function on is called (completely) -additive if , where and . We prove that the values are asymptotically equidistributed on the (finite) image set if are pairwise coprime and are -additive. Furthermore, it is shown that are asymptotically independent and Gaussian if are - resp. -additive.
-uniform distribution of entire functions
Block additive functions on the Gaussian integers
On a mixed Littlewood conjecture in Diophantine approximation
Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture
We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.
Page 1