Publications from the SFB in the different periods

Publications from 01.01.2018 until today

  1. Drmota M., Mauduit C., Rivat J.: The Thue Morse Sequence along Squares is Normal, Submitted. Pdf.
  2. Saad Eddin S.: An asymptotic distribution for $|L^\prime/L(1,\chi)|$, Submitted. arXiv:1503.08353.
  3. Irrgeher C., Kritzer P., Pillichshammer F.:  Integration and approximation in cosine spaces of smooth functions. In: Math. Comput. Simulation, 143, pp. 35-45, 2018.. arXiv:1511.00328.
  4. Kritzinger R.: An exact formula for the $L_2$ discrepancy of the symmetrized Hammersley point set. In: Math. Comput. Simulat., 2018. arXiv:1509.01818.
  5. Hofer R.: Halton-Type Sequences in Rational Bases in the Ring of Rational Integers and in the Ring of Polynomials over a Finite Field. In: Proceedings of the 10th IMACS Seminar on Monte Carlo Methods, Mathematics and Computers in Simulation, 143, pp. 78-88, 2018. Pdf.
  6. Madritsch M., Tichy, R.: Dynamical systems and uniform distribution of sequences. In: Memorial Volume for Wolfgang Schwarz, Springer International Publishing Switzerland, to appear, arXiv:1501.07411.
  7. Grepstad S., Lev N.: Riesz bases, Meyer's quasicrystals, and bounded remainder sets. In: Transactions of the AMS, to appear. arXiv:1602.00495.
  8. Agora E., Grepstad S., Kolountzakis M.N.: Spectra for cubes in products of finite cyclic groups. In: Proceedings of the AMS, to appear. arXiv:1602.03165.
  9. Kritzer P., Pillichshammer F., Wasilkowski G.W.: Truncation Dimension for Function Approximation. In: Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Woźniakowski, eds.), Springer-Verlag, pp. 771-792, 2018. arXiv:1610.02852.
  10. Hittmeir M.: Computational aspects of rational residuosity. In: International Journal of Number Theory, to appear. arXiv:1604.07791.
  11. Kreso D., Tichy R.: Diophantine equations and monodromy groups. In: Period. Math. Hungar., to appear. arXiv:1601.07316.
  12. Hales T., Kusner W.: Packings of Regular Pentagons in the Plane, Submitted, 2016. arXiv:1602.07220.
  13. Dick J., Irrgeher C., Leobacher G., Pillichshammer F.: On the optimal order of integration in Hermite spaces with finite smoothness. In: SIAM Journal on Numerical Analysis, 56(2), pp. 684-707, 2018. arXiv:1608.06061.
  14. Dick J., Pillichshammer F., Suzuki K., Ullrich M., Yoshiki T.: Lattice based integration algorithms: Kronecker sequences and rank-1 lattices. In: Ann. Mat. Pura Appl., 197, no. 1, pp. 109--126, 2018. arXiv:1608.08687.
  15. Aistleitner Ch., Larcher G., Pillichshammer F., Saad Eddin S., Tichy R.F.: On Weyl products and uniform distribution modulo one. In: Monatsh. Math., 185(3), pp. 365-395, 2018. arXiv:1609.04929.
  16. Leobacher G., Szölgyenyi M.: Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. In: Nummerische Mathematik, 138(1), pp. 219-239, 2018. arXiv:1610.07047.
  17. Bors A.: Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements. Submitted, 2016. Pdf.
  18. Aichinger I., Aistleitner C., Larcher G.: On quasi-energy-spectra, pair correlations of sequences and additive combinatorics. In:  Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Wozniakowski, eds.), Springer-Verlag, pp. 1-16, 2018. Pdf.
  19. Kritzer P., Laimer H., Pillichshammer F.: Tractability of $L_2$-approximation in hybrid function spaces. In: Funct. Approx. Comment. Math., 58(1), pp. 89-104, 2018. arXiv:1701.02910.
  20. Kritzinger R.: Optimal discrepancy rate of point sets in Besov spaces with negative smoothness. In: Proceedings of the MCQMC 2016, to appear. arXiv:1701.01970.
  21. Hinrichs A., Kritzer P., Pillichshammer F., and Wasilkowski G.W.: Truncation dimension for linear problems on multivariate function spaces. In: Numer.Alg., to appear. arXiv:1701.06778
  22. Drmota M., Müllner C., Spiegelhofer L.: Möbius orthogonality of the Zeckendorf sum-of-digits function. In: Proc. Amer. Math. Soc., Submitted, 2016. arXiv:1706.09680.
  23. Hackmann D.: Karhunen-Loève expansions of Lévy processes. In: Communications in Statistics - Theory and Methods, to appear. arXiv:1603.00677.
  24. Kusner R., Kusner W., Lagarias J.C., Shlosman S.: The twelve spheres problem, Submitted, 2016. arXiv:1611.10297.
  25. Hittmeir M.: A babystep-giantstep method for faster deterministic integer factorization. In: Mathematics of Computation, to appear. arXiv:1608.08766.
  26. Hellekalek P.: On the $3x+1$ problem. Submitted, 2016. arXiv:1605.02634.
  27. Preischl M.: Bounds on integrals with respect to multivariate copulas, Submitted, 2016. arXiv.1606.08661.
  28. Neumüller M., Pillichshammer F.: Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. In: Unif. Distrib. Theory, 13(1), pp. 65-86, 2018. arXiv:1605.00378.
  29. Madritsch M., Scheerer A.M., Tichy R.: Computable absolutely Pisot normal numbers. to appear. arXiv:1610.06388.
  30. Madritsch M., Tichy R.: Multidimensional Heilbronn sets, Submitted, 2016. arXiv:1606.03049.
  31. Ghosh A., Marnat A.: On diophantine transference principles, Submitted, 2016. arXiv:1610.02161.
  32. Kerber M., Tichy R., Weitzer M.: Constrained triangulations, volumes of polytopes and unit equations. In: 33rd International Symposium on Computational Geometry (SoCG 2017), to appear. arXiv:1609.05017.
  33. Müllner C.: The Rudin-Shapiro sequence and similar sequences are normal along squares, Submitted, 2017. arXiv:1704.06472.
  34. Kritzinger R., Laimer H., Neumüller M.: A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy. In: Proceedings of the MCQMC 2016, to appear. arXiv:1701.02525.
  35. Spiegelhofer L.: A digit reversal property for Stern polynomials. Submitted, 2017. arXiv:1610.00108.
  36. Spiegelhofer L.: Pseudorandomness of the Ostrowski sum-of-digits function. Submitted, 2017. arXiv:1611.03043.
  37. Coons M., Spiegelhofer L.: Number theoretic aspects of regular sequences. Submitted, 2017. link.
  38. Greinecker F.: Equidistribution on fractals. In: J. Fractal Geom., to appear. Pdf.
  39. Grabner P.: A note on some approximation kernels on the sphere. In: Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Woźniakowski, eds.), Springer-Verlag, pp. 443-453, 2018. arXiv:1706.09456.
  40. Derfel G., Grabner P., Tichy R.: On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling. In: J. Operator Theory, to appear. arXiv:1612.06226.
  41. Aichinger I., Larcher G.: Sets of Bounded Remainder for the Billiard on a Square. In: Uniform Distribution Theory,  to appear. Pdf.
  42. Puchhammer F.: On an explicit lower bound for the star discrepancy in three dimensions. In: Mathematics and Computers in Simulation, to appear. arXiv:1602.01307.
  43. Marnat A.: Note on the spectrum of classical and uniform exponents of diophantine approximation, Submitted, 2017. arXiv:1701.01584.
  44. Roche-Newton O., Shparlinski I.E., and Winterhof A.: Analogues of the Balog-Wooley decomposition for subsets of finite fields and character sums with convolutions. In: Annals of Combinatorics, to appear. arXiv:1702.04590.
  45. Mérai L., Winterhof A.: On the Nth linear complexity of $p$-automatic sequences over $F_p$, Submitted. Pdf.
  46. Roche-Newton O., Winterhof A.: Packing sets over finite fields. In: Integers, to appear. arXiv:1611.00529.
  47. Saad Eddin S.: Applications of the Laurent-Stieltjes constants for Dirichlet L-series. In: Proc. Japan. Academy (Series A), to appear. arXiv:1705.03596.
  48. Kreso D., Tichy R.: Diophantine equations in separated variables and lacunary polynomials. In: Periodica Math. Hungarica, to appear.
  49. Kritzer P. , Kuo F.Y., Nuyens D., Ullrich M.: Lattice rules with random $n$ achieve nearly the optimal $\mathcal{O}(n^{-\alpha-1/2})$ error independently of the dimension. Submitted, 2017. arxiv:1706.04502.
  50. Hofer R., Pirsic I.: An extension of the digital method based on $b$-adic integers. In: Uniform Distribution Theory, 13(1), pp. 87 - 107, 2018. arXiv:1706.06323v2.
  51. Isik L., Winterhof A.: Carlitz rank and index of permutation polynomials. In: Finite Fields and Their Applications, to appear. arXiv:1611.06361.
  52. Saad Eddin S.: The signs of the Stieltjes constants associated with the Dedekind zeta function. Submitted, 2017. arXiv:1707.01622.
  53. Preischl M., Thonhauser S., Tichy R.: Integral Equations, Quasi-Monte Carlo Methods and Risk Modeling. In: Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Woźniakowski, eds.), Springer-Verlag, pp. 1051-1074, 2018. arXiv:1707.03655.
  54. Z. Sun, A. Winterhof: On the maximum order complexity of the Thue-Morse and Rudin-Shapiro sequence. Submitted, 2017. Pdf.
  55. Hofer R.: A metric result for special sequences related to the Halton sequences. In: Journal of Complexity 44, pp. 23-29, 2018. arXiv:1708.05577.
  56. Kritzer P., Pillichshammer F., Wasilkowski G.W.: Truncation in average and worst case settings for special classes of $\infty$-variate functions. Submitted, 2017. arXiv:1709.02113.
  57. Luca F., Moree P., Osbum R., Saad Eddin S., Sedunova A.: Constrained ternary integers. In: International Journal of Number Theory, to appear. arXiv:1710.08403.
  58. Hofer R., Puchhammer F.: On the discrepancy of two-dimensional perturbed Halton-Kronecker sequences and lacunary trigonometric products. In: Acta Arithmetica (180), pp. 365-392, 2017. Pdf.
  59. Hefter M., Herzwurm A., Müller-Gronbach Th.: Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients. Submitted, 2017. arXiv:1710.08707.
  60. Kritzer P., Niederreiter H., Pillichshammer F.: Ian Sloan and Lattice Rules. In: Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Woźniakowski, eds.), Springer-Verlag, pp. 741-769, 2018. Pdf.
  61. Pillichshammer F.: Tractability properties of the weighted star discrepancy of regular grids. In: J. Complexity 46, pp. 103-112, 2018. arXiv:1710.00573.
  62. Dick J., Pillichshammer F., Suzuki K., Ullrich M., Yoshiki T.: Digital net properties of a polynomial analogue of Frolov's construction. In: Finite Fields Appl. 51, pp. 325-350, 2018. arXiv:1712.06831.
  63. Kritzer P., Leobacher G., Szölgyenyi M., Thonhauser S.: Approximation methods for piecewise deterministic Markov processes and their costs. Submitted, 2017. arXiv:1712.09201.
  64. Kiuchi I., Saad Eddin S.: On sums of weighted averages of $\gcd$-sum functions. In: International Journal of Number Theory, to appear. arXiv:1801.03647.
  65. Kiuchi I., Saad Eddin S.: Sums of $\gcd$-sum functions with weights concerning the Gamma function and Bernoulli polynomials, Submitted, 2018. arXiv:1801.03653.
  66. Serdyuk A.S., Stepanyuk T.A.: Uniform approximations by Fourier sums on  classes of generalized Poisson integrals. In: Analysis Mathematica, to appear. Pdf.
  67. Hofer R.: Kronecker-Halton sequences in $\mathbb{F}_{p} ((X^{-1}))$. In: Finite Fields and Their Applications 50, pp. 154-177, 2018. arXiv:1709.06432.
  68. Brauchart J., Grabner P., Kusner W.: Hyperuniform point sets on the sphere: deterministic constructions. Submitted, 2017. arXiv: 1709.02613.
  69. Grabner P., Stepanyuk T.A.: Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension. Submitted, 2018. arXiv: 1801.05474.
  70. Pethő A., Thuswaldner J., Weitzer M.: Shift radix systems with general parameters. Submitted, 2017. arXiv:1711.09596.
  71. Mahadi D., Gómez C.A., Luca F.: On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2. In: Monatshefte für Mathematik, 1436-5081, 2018. doi: 10.1007/s00605-018-1155-1. Link.
  72. Grepstad S., Neumüller M.: Asymptotic Behaviour of the Sudler Product of Sines for Quadratic Irrationals. In: Journal of Mathematical Analysis and Applications, to appear. arXiv:1801.09416.
  73. Kritzer P., Niederreiter H., Pillichshammer F.: Ian Sloan and Lattice Rules. In: Festschrift for Ian Sloan's 80th birthday, Springer. Link.
  74. Matsumoto K., Saad Eddin S.:  An asymptotic formula for the 2k-th power mean value of $|(L'/L)(1+it_0,\chi)|$, Submitted, 2018. arXiv:1803.00495.
  75. Kaltenböck L., Stockinger W.: A survey on M. B. Levins proofs for the exact lower discrepancy bounds of special sequences and point sets. In: Uniform Distribution Theory, to appear. arXiv:1708.03189.
  76. Pirsic I., Stockinger W.: The Champernowne constant is not Poissonian. In: Functiones et Approximatio Commentarii Mathematici, to appear. arXiv:1710.09313.
  77. Larcher G., Stockinger W.: Pair correlation of sequences $(\left\{a_{n}\alpha\right\})_{n \varepsilon\mathbb{N}}$ with maximal order of additive energy, Submitted, 2018. arXiv:1802.02901.
  78. Larcher G., Stockinger W.: Some negative results related to Poissonian pair correlation problems, Submitted, 2018. arXiv:1803.05236.
  79. Kiuchi I., Saad Eddin S.: On sums of logarithmic averages of gcd-sum functions, Submitted, 2018. arXiv:1804.01902.
  80. Ebert, A., Kritzer, P.: Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm. Submitted, 2018. arXiv:1804.01765.
  81. Kritzinger R., Pillichshammer F.: Digital nets in dimension two with the optimal order of $L_p$ discrepancy. Submitted, 2018. arXiv:1804.04891.
  82. Saad Eddin S.: A survey on the evaluation of the values of Dirichlet $L$-functions and of their logarithmic derivatives at $1+it_0$, Submitted, 2018. Pdf.
  83. Kiuchi I., Saad Eddin S.: On the unitary and bi-unitary analogues of generalized Ramanujan sums, Submitted, 2018. Pdf.
  84. Kritzinger R.: Finding exact formulas for the $L_2$ discrepancy of digital $(0,n,2)$-nets via Haar functions. In: Acta Arithmetica, to appear. arXiv:1711.06058.
  85. Anbar Meidl N.: Shifted plateaued functions, Submitted, 2018. Pdf.
  86. Kritzer, P., Wozniakowski, H.: Notes on tractability conditions for linear multivariate problems. Submitted, 2018. arXiv: 1807.03055.
  87. Hofer R., Suzuki K.: Characterization of digital $(0,m,3)$-nets and digital $(0,2)$-sequences in base $2$, Submitted, 2018. arXiv:1807.04383.

Publications in the period 01.01.2017-31.12.2017: list

Publications in the period 01.01.2016-31.12.2016: list

Publications in the period 01.01.2015-31.12.2015: list

Publications in the period 01.02.2014-31.12.2014: list

Books in the period 01.02.2014-31.07.2017:

  1. Saad Eddin S.: Two problems with Laurent-Stieltjes coefficients. LAP Lambert Academic Publishing. 2017.
  2. Kritzer P., Niederreiter H., Pillichshammer F., Winterhof A. (eds.): Uniform Distribution and Quasi-Monte Carlo Methods: Discrepancy, Integration and Applications. Radon Series on Computational and Applied Mathematics (15) Berlin. 2014.
  3. Larcher G., Pillichhammer F., Winterhof A., Xing C. (eds.): Applied Algebra and Number Theory. Essays in honor of Harald Niederreiter on the occasion of his 70th birthday. Cambridge: Cambridge University Press, 2014.
  4. Leobacher G., Pillichshammer F.: Introduction to Quasi-Monte Carlo Integration and Applications. Birkhäuser. 2014.
  5. Niederreiter H., Ostafe A., Panario D., Winterhof A. (eds.) Algebraic Curves and Finite Fields: Cryptography and Other Applications. Radon Series on Computational and Applied Mathematics (16), De Gruyter, Berlin. 2014.
  6. Schmidt K.-U., Winterhof A. (eds.): Sequences and Their Applications-SETA 2014. Lecture Notes Computer Science: Springer. 2014.
  7. Niederreiter H., Winterhof A.: Applied Number Theory, Berlin: Springer. 2015.
  8. Elsholtz C. and Grabner P.J. (eds): Number Theory – Diophantine Problems, Uniform Distribution and Applications. Festschrift on the occasion of Robert Tichy's 60th birthday. Springer, 2017.

PhD Theses in the period  01.02.2014-31.07.2017:


  • Michaela Szölgyenyi: Dividend Maximization in Hidden Markov Models and Analysis of Associated Stochastic Differential Equations. 2015. (Supervisor: Gunther Leobacher and Stefan Thonhauser) Link.
  • Ralph Kritzinger: Point sets and sequences with the optimal order of Lp<math xmlns=""><msub><mi>L</mi><mi>p</mi></msub></math> discrepancy. 2017. (Supervisor: Friedrich Pillichshammer) Pdf.
  • Florian Puchhammer: Discrepancy estimates for point sets and sequences. 2017. (Supervisor: Gerhard Larcher) Pdf.
  • Richard Hofer: New Bounds on Some Measures of Pseudorandomness. 2017. (Supervisor: Arne Winterhof) Pdf.
  • Helene Laimer. High-dimensional algorithms - Tractability and componentwise constructions. 2017. (Supervisor: Peter Kritzer) Pdf.