### 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 9:

Diophantine approximation and combinatorial problems

#### Publications 2018

[64] | Diophantine approximation: Analytic and geometric methods, PhD thesis, TU Graz, (2018).
[bib] | ,

[63] | The Duffin-Schaeffer conjecture with extra divergence, preprint, (2018).
[bib] [arXiv] | ,

[62] | The Duffin-Schaeffer Conjecture with Extra Divergence, (2018). (preprint)
[bib] [arXiv] | ,

[61] | On linear relations for Dirichlet series formed by recursive sequences of second order, preprint, (2018).
[bib] [arXiv] | ,

[60] | On a variant of Pillai's problem II, J. Number Theory, 183, (2018).
[bib] [arXiv] [MR] [doi/article] | ,

[59] | Linear forms in logarithms and applications to Diophantine problems, PhD thesis, TU Graz, (2018).
[bib] | ,

[58] | There is no Khintchine threshold for metric pair correlations, (2018). (preprint)
[bib] [arXiv] | ,

[57] | Computable absolutely Pisot normal numbers, Acta Arithmetica, (2018). (to appear)
[bib] [arXiv] [doi/article] | ,

[56] | Diophantine equations in separated variables, Period. Math. Hungar., 76(1), 47-67, (2018).
[bib] [arXiv] [doi/article] | ,

[55] | On the $x$-coordinates of Pell equations which are $k$-generalized Fibonacci numbers, (2018). (preprint)
[bib] [arXiv] | ,

[54] | On a problem of Pillai with $k$--generalized Fibonacci numbers and powers of $2$, Monatshefte für Mathematik, (2018).
[bib] [arXiv] [doi/article] | ,

#### Publications 2017

[53] | A Loewner Equation for Infinitely Many Slits, Computational Methods and Function Theory, 17, 255-272, (2017).
[bib] [MR] [doi/article] | ,

[52] | Dynamical systems and normal numbers -- qualitative and computational aspects, PhD thesis, TU Graz, (2017).
[bib] | ,

[51] | Computable Absolutely Normal Numbers and Discrepancies, Math. Comp., 86, 2911-2926, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[50] | On Exceptional Sets in the Metric Poissonian Pair Correlations problem, (2017). (preprint)
[bib] [arXiv] | ,

[49] | The maximal order of iterated multiplicative functions, (2017). (preprint)
[bib] [arXiv] | ,

[48] | On Diophantine equations involving sums of Fibonacci numbers and powers of 2, (2017). (preprint)
[bib] [arXiv] | ,

[47] | On a variant of Pillai's problem, Int. J. Number Theory, 13, 1711-1727, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[46] | Squares with three nonzero digits, Chapter in Number theory---Diophantine problems, uniform distribution and applications (C. Elsholtz, P. Grabner, eds.), Springer, Cham, 83—108, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[45] | On the construction of absolutely normal numbers, Acta Arith., 180(4), 333—346, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[44] | Constrained Triangulations, Volumes of Polytopes, and Unit Equations, Chapter in 33rd International Symposium on Computational Geometry (SoCG 2017) (Boris Aronov, Matthew J. Katz, eds.), 77, 46:1—46:15, (2017).
[bib] [doi/article] | ,

[43] | Diophantine equations in separated variables and lacunary polynomials, Int. J. Number Theory, 13(9), 2055-2074, (2017).
[bib] [MR] [doi/article] | ,

[42] | On the regularity of primes in arithmetic progressions, Int. J. Number Theory, 13(5), 1349-1361, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

[41] | On a problem of Pillai with Fibonacci numbers and powers of $2$, Proc. Indian Acad. Sci. (Math. Sci.), 127(3), 411-421, (2017).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2016

[40] | On a Counting Theorem of Skriganov, (2016).
[bib] [arXiv] | ,

[39] | Diophantine equations with truncated binomial polynomials, Indag. Math., 27(1), 392-405, (2016).
[bib] [MR] [doi/article] | ,

[38] | Multidimensional van der Corput sets and small fractional parts of polynomials, (2016). (preprint)
[bib] [arXiv] | ,

[37] | Linear recursive odometers and beta-expansions, Unif. Distrib. Theory, 11(1), 175—186, (2016).
[bib] [MR] [doi/article] | ,

[36] | Fibonacci numbers which are products of two Pell numbers, The Fibonacci Quarterly, 54(1), 11-18, (2016).
[bib] [arXiv] [MR] [doi/article] | ,

[35] | The Kadec-Pełczyński theorem in $L^p$, $1\leq p<2$, Proc. Amer. Math. Soc., 144(5), 2053—2066, (2016).
[bib] [MR] [doi/article] | ,

[34] | An extremal problem in uniform distribution theory, Uniform distribution theory, 11(2), 1-21, (2016).
[bib] | ,

#### Publications 2015

[33] | Normality in Pisot numeration systems, Ergodic Theory and Dynamical Systems, 1-9, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[32] | On common values of lacunary polynomials at integer points, New York J. Math., 21, 987—1001, (2015).
[bib] [MR] [doi/article] | ,

[31] | Measure density for set decompositions and uniform distribution, Rend. Circ. Mat. Palermo (2), 64(2), 323—339, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[30] | Additive decompositions of sets with restricted prime factors, Trans. Amer. Math. Soc., 367(10), 7403—7427, (2015).
[bib] [MR] [doi/article] | ,

[29] | On conjectures and problems of Ruzsa concerning difference graphs of S-units, Acta Math. Hungar., 146, 391-404, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[28] | The asymptotic distribution function of the 4-dimensional shifted van der Corput sequence, Tatra Mt. Math. Publ., 64, 75—92, (2015).
[bib] [MR] [doi/article] | ,

[27] | On permutation-invariance of limit theorems, J. Complexity, 31(3), 372—379, (2015).
[bib] [MR] [doi/article] | ,

[26] | Lacunary series and stable distributions, Chapter in Mathematical statistics and limit theorems, Springer, Cham, 7—19, (2015).
[bib] [MR] [doi/article] | ,

[25] | Algebraic $S$-integers of fixed degree and bounded height, Acta Arithmetica, 167(1), 67—90, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[24] | Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials, Grazer Math. Ber., 363, 143—170, (2015).
[bib] [arXiv] [MR] | ,

[23] | Distribution functions, extremal limits and optimal transport, Indag. Math. (N.S.), 26(5), 823—841, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2014

[22] | On factorizations of maps between curves, (2014). (preprint)
[bib] [arXiv] | ,

[21] | Rational function decomposition and Diophantine equations, PhD thesis, TU Graz, (2014).
[bib] [doi/article] | ,

[20] | Low discrepancy sequences: theory and applications, PhD thesis, Università della Calabria, (2014). ((cotutelle with TU Graz))
[bib] [arXiv] | ,

[19] | Optimal bounds for integrals with respect to copulas and applications, Journal of Optimization Theory and Applications, 161, 999-1011, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[18] | On Diophantine quintuples and $D(-1)$-quadruples, Monatshefte für Mathematik, 175, 227-239, (2014).
[bib] [MR] [doi/article] | ,

[17] | A dynamical system approach to the Kakutani-Fibonacci sequence, Ergodic Theory Dynam. Systems, 34(6), 1794—1806, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[16] | Counting lattice points and o-minimal structures, International Mathematics Research Notices, 2014, 4932-4957, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[15] | Counting algebraic integers of fixed degree and bounded height, Monatshefte für Mathematik, 175, 25-41, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2013

[14] | Diophantine equations with Euler polynomials, Acta Arithmetica, 161, 267—281, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[13] | Ergodic properties of $\beta$-adic Halton sequences, Ergodic Theory and Dynamical Systems, 35, 895—909, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[12] | Sumsets being squares, Acta Mathematica Hungarica, 141(4), 353-357, (2013).
[bib] [MR] [doi/article] | ,

[11] | On gaps between primitive roots in the Hamming metric., Quarterly Journal of Mathematics, 64(4), 1043—1055, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[10] | Counting lattice points, o-minimal structures and applications, PhD thesis, TU Graz, (2013).
[bib] [doi/article] | ,

#### Publications 2012

[9] | On equal values of power sums of arithmetic progressions, Glasnik Matematički, 47(2), 253—263, (2012).
[bib] [arXiv] [MR] | ,

[8] | On the system $f(nx)$ and probabilistic number theory. Analytic and probabilistic methods in number theory, In Proceedings of the 5th International Conference in honour of J. Kubilius held in Palanga, TEV, 1-18, (2012).
[bib] [arXiv] [MR] | ,

[7] | On the law of the iterated logarithm for permuted lacunary sequences, Proceedings of the Steklov Institute of Mathematics, 276, 3-20, (2012).
[bib] [arXiv] [MR] | ,

#### Publications 2011

[6] | Nonextensibility of the pair $\lbrace 1, 3\rbrace$ to a Diophantine quintuple in ${\mathbb Z}[\sqrt{2}]$, Journal of Combinatorics and Number Theory, 3(3), 1-15, (2011).
[bib] [arXiv] [MR] | ,

[5] | Sum of units in number fields and function fields, PhD thesis, TU Graz, (2011).
[bib] [doi/article] | ,

[4] | Additive unit representations in rings over global fields -- A survey, Publicationes Mathematicae Debrecen, 79(3-4), 291-307, (2011).
[bib] [arXiv] [MR] | ,

[3] | On the asymptotic behavior of weakly lacunary sequences, Proceedings of the American Mathematical Society, 139, 2505-2517, (2011).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2010

[2] | Dependence in Probability, Analysis and Number Theory, (István Berkes, Richard C. Bradley, Herold Dehling, Magda Peligrad, Robert Tichy, eds.), Kendrick Press, Heber City, UT, iv+353, (2010).
[bib] |

#### Publications 201?

[1] | On the continued fraction expansion of absolutely normal numbers, J. Th. Nombres Bordeaux, (201?). (to appear)
[bib] [arXiv] | ,