Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

    Austrian Science Fund (FWF): W1230

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

Project 4:
Point distributions and fractal analysis

2014
[18]Peter J. Grabner, Point sets of minimal energy, Chapter in Applied algebra and number theory (Gerhard Larcher, others, eds.), Cambridge Univ. Press, Cambridge, 109-125, (2014). [bibtex] [pdf]
[17]Peter J. Grabner, Arnold Knopfmacher and Stephan G. Wagner, A general asymptotic scheme for the analysis of partition statistics, Combinatorics, Probability and Computing, 23(6), 1057-1086, (2014). [bibtex] [doi]
2015
[16]Johann S. Brauchart and Peter J. Grabner, Distributing many points on spheres: minimal energy and designs, Journal of Complexity, 31(3), 293–326, (2015). [bibtex] [doi]
[15]Peter J. Grabner, Poincaré functional equations, harmonic measures on Julia sets, and fractal zeta functions, In Fractal Geometry and Stochastics V (Christoph Bandt, others, eds.), Birkhäuser Verlag, 70, 157-174, (2015). [bibtex] [pdf]
[14]Florian Greinecker, On the 2-abelian Complexity of the Thue-Morse word, Theoretical Computer Science, 593, 88-105, (2015). [bibtex] [doi]
[13]Florian Greinecker, Combinatorial and number theoretic properties of certain automatic sequences, PhD thesis, TU Graz, (2015). [bibtex] [url]
2016
[12]Guy Barat and Peter Grabner, Spatial equidistribution of binomial coefficients modulo prime powers, Uniform Distribution Theory, 11(2), 151-161, (2016). [bibtex] [pdf]
[11]Guy Barat and Peter Grabner, Combinatorial and probabilistic properties of systems of numeration, Ergodic Theory and Dynamical Systems, 36(2), 422–457, (2016). [bibtex] [pdf] [doi]
2017
[10]Number theory—Diophantine problems, uniform distribution and applications, (Christian Elsholtz, Peter Grabner, eds.), Springer, xv+444, (2017). (Festschrift in honour of Robert F. Tichy's 60th birthday) [bibtex] [doi]
[9]Florian Greinecker, Spatial equidistribution of combinatorial number schemes, Journal of Fractal Geometry, 4(2), 105–126, (2017). [bibtex] [pdf] [doi]
2018
[8]Gregory Derfel, Peter J. Grabner and Robert F. Tichy, On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling, Chapter in Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations, Springer, 281–295, (2018). [bibtex]
[7]Peter J. Grabner, A Note on Some Approximation Kernels on the Sphere, Chapter in Contemporary Computational Mathematics — A Celebration of the 80th birthday of Ian Sloan (J. Dick, others, eds.), Springer Verlag, 443–453, (2018). [bibtex] [doi]
2019
[6]Johann S. Brauchart, Peter J. Grabner and Wöden B. Kusner, Hyperuniform point sets on the sphere: deterministic aspects, Constr. Approx., 50, 45-61, (2019). [bibtex] [doi]
[5]Peter J. Grabner and Tetiana A. Stepanyuk, Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension, Journal of Complexity, 53, 113 - 132, (2019). [bibtex] [doi]
2020
[4]Carlos Beltrán and Damir Ferizović, Approximation to uniform distribution in SO(3), Constructive Approximation, 52(2), 283–311, (2020). [bibtex] [doi]
2021
[3]Damir Ferizović, On the $L^2$-norm of Gegenbauer polynomials, Mathematical Sciences, (2021). [bibtex] [doi]
[2]Damir Ferizović, Uniform point distributions and energy estimates on compact Riemannian manifolds, PhD thesis, TU Graz, (2021). [bibtex] [url]
2022
[1]Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin, Ryan Matzke, Josiah Park and Oleksandr Vlasiuk, Potential theory with multivariate kernels, Mathematische Zeitschrift, (2022). [bibtex] [doi]