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Quasi-Monte Carlo Methods: Theory and Applications

FWF Special Research Program (SFB)

Publications from the SFB in the different periods

Publications in the period 01.01.2021 until today


  1. Hales T., Kusner W.: Packings of Regular Pentagons in the Plane. In: Contemporary Mathematics, to appear. arXiv:1602.07220.
  2. Hellekalek P.: On the $3x+1$ problem. Submitted, 2016. arXiv:1605.02634.
  3. Pethő A., Thuswaldner J., Weitzer M.: Shift radix systems with general parameters. Submitted, 2017. arXiv:1711.09596.
  4. Matsumoto K., Saad Eddin S.:  An asymptotic formula for the 2k-th power mean value of $|(L'/L)(1+it_0,\chi)|$. In: Journal of the Mathematical Society of Japan, to appear. arXiv:1803.00495.
  5. Kiuchi I., Saad Eddin S.: On the unitary and bi-unitary analogues of generalized Ramanujan sums. In: Tbilisi Mathematical journal, to appear. PDF.
  6. Kiuchi I., Pillichshammer F., Saad Eddin S.: On the multivariable generalization of Anderson-Apostol sums. In: Far East Journal of Mathematical Sciences, to appear. arXiv:1811.06022.
  7. Keryan K., Passenbrunner M.: Projection operators onto spaces of Chebyshev splines, Submitted, 2018. arXiv:1807.07161.
  8. Leobacher G., Steinicke A.: Existence, Uniqueness and Regularity of the Projection onto Differentiable Manifolds, Ann. Glob. Anal. Geom. (2021), to appear, arXiv:1811.10578.
  9. Anbar Meidl N., Stichtenoth H., Tutdere S.: Asymptotically good towers of function fields with small $p$-rank, Submitted, 2019. PDF.
  10. Aistleitner C., Blomer V., Radziwill M.: Triple correlation and long gaps in the spectrum of flat tori, submitted, 2018, arXiv:1809.07881.
  11. Dong G. Y., Lemieux C., Wiart J.: On the dependence structure of scrambled (t, m, s)-nets. Submitted, 2019. arXiv:1903.09877
  12. Languasco A., Moree P., Saad Eddin S., Sedunova A.: Computation of the Kummer ratio of the class number for prime cyclotomic fields, Submitted, 2019. arXiv:1908.01152.
  13. Inoue S., Saad Eddin S., Suriajaya A.I.: Stieltjes constants of $L$-functions in the extended Selberg class. In: Ramanujan J., to appear. DOI:10.1007/s11139-021-00391-1
  14. Serdyuk A., Stepaniuk T.: Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals, In: Filomat, to appear. arXiv:1908.09517.
  15. Hinrichs A., Krieg D., Novak E., Prochno J., Ullrich M.: Random sections of ellipsoids and the power of random information. In: Transactions of the AMS, to appear. arXiv:1901.06639.
  16. Krieg D., Ullrich M.: Function values are enough for $L_2$-approximation. In: Foundations of Computational Mathematics, to appear. arXiv:1905.02516.
  17. Krieg D., Ullrich M.: Function values are enough for $L_2$-approximation: Part II, Submitted. arXiv:2011.01779.
  18. Grabner P. J.: Purity results for some arithmetically defined measures, Submitted, 2019. arXiv:1908.09023.
  19. Johnston S., Prochno J.: A Maxwell principle for generalized Orlicz balls, Submitted, 2020. arXiv:2012.11568.
  20. Alonso-Gutiérrez D., Prochno J.: Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures, Submitted, 2020. arXiv:2011.07523.
  21. Ebert A., Kritzer P., Nuyens D., Osisiogu O.: Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness. In: J. Complexity, 2021.   arXiv:2001.02978v1 
  22. Serdyuk A.S., Stepanyuk T.: Uniform approximations by Fourier sums on classes of convolutions of periodic functions, Submitted, 2020. arXiv:2001.00374v1
  23. Wiart, J., Wong, E.: An application of symbolic computation to quasi-Monte Carlo integration. In: Mathematics and Computers in Simulation, Bd. 182, S. 277-295, 2021. arXiv:2006.06225v1
  24. Desmettre S., Wahl M., Zagst R.: Dynamic Surplus Optimization with Performance- and Index-Linked Liabilities, Submitted, 2020. Link.
  25. Kaltenböck L., Kiuchi I., Saad Eddin S. and Ueda M.: Sums of averages of gcd-sum functions II, In: Results in Mathematics, 76(43), 2021. DOI: 10.1007/s00025-021-01357-x.
  26. Kiuchi I. and Saad Eddin S.: On the weighted average number of subgroups of ${\mathbb {Z}}_{m}\times {\mathbb {Z}}_{n}$ with $mn\leq x$, Submitted, 2020. arXiv:2008.07850.
  27. Ebert A., Kritzer P., Osisiogu O., Stepaniuk T.: Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces. In: Constr. Approx., to appear. arXiv:2008.08966
  28. Hofer R.: Finding both, the continued fraction and the Laurent series expansion of golden ratio analogs in the field of formal power series. In: Journal of Number Theory, to appear, 2021. arXiv:2008.04518
  29. Kritzer P., Pillichshammer F., Wasilkowski G.W.: On quasi Monte Carlo methods in weighted ANOVA spaces, In: Mathematics of Computation 90, 1381--1406, 2021. arXiv:2001.05765
  30. Pillichshammer F.: A note on Korobov lattice rules for integration of analytic functions, In: J. Complexity, 63,101524, 2021. arXiv:2010.03286
  31. Sonnleitner M., Pillichshammer F.: On the relation of the spectral test to isotropic discrepancy and $L_q$-approximation in Sobolev spaces. In: J. Complexity, to appear. arXiv:2010.04522.
  32. Desmettre S., Leobacher G., Rogers L.C.G.: Change of drift in one-dimensional diffusions, In: Finance and Stochastics, 25(2), pp. 359-381, 2021.
  33. Hinrichs A., Kritzinger R., Pillichshammer F.: Extreme and periodic $L_2$ discrepancy of plane point sets, In: Acta Arith., to appear. arXiv:2005.09933.
  34. Drmota M., Mauduit C., Rivat J., Spiegelhofer L.: Möbius orthogonality for sequences with maximal entropy, In: J. Anal. Math., to appear. arXiv:2001.07898.
  35. Spiegelhofer L.: A lower bound for Cusick's conjecture on the digits of n+t, In: Math. Proc. Cambridge Philos. Soc., to appear. arXiv:1910.13170.
  36. Spiegelhofer L.: The level of distribution of the Thue--Morse sequence, In: Compos. Math., to appear. arXiv:1803.01689.
  37. Amri M., Spiegelhofer L., Thuswaldner J.: Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidu, Submitted. arXiv:2006.06960.
  38. Spiegelhofer L., Wallner M.: The digits of n+t, Submitted. arXiv:2005.07167.
  39. Adamczewski B., Drmota M., Müllner C.: (Logarithmic) densities for automatic sequences along primes and squares. In: Transactions AMS, to appear. arXiv:2009.14773.
  40. Gillibert P., Lachmann T., Müllner C.: The VC-Dimension of Axis-Parallel Boxes on the Torus, Submitted. arXiv:2004.13861.
  41. Drmota M., Verwee J.: Effective Erdos-Wintner Theorems for Digital Expansions. In: Journal of Number Theory, to appear. arXiv:2009.05435.
  42. Aistleitner C., Technau N., Zafeiropoulos A.: On the order of magnitude of Sudler products, Submitted. arXiv:2002.06602.
  43. Aistleitner C., Borda B.: Quantum invariants of hyperbolic knots and extreme values of trigonometric products, Submitted. arXiv:2006.08578.
  44. Aistleiter C., El-Baz D., Munsch M.: A pair correlation problem, and counting lattice points with the zeta function. In: Geom. Funct. Anal., to appear. arXiv:2009.08184.
  45. Aistleiter C., Baker S., Technau N., Yesha N.: Gap statistics and higher correlations for geometric progressions modulo one, Submitted. arXiv:2010.10355.
  46. Aistleiter C., Gantert N., Kabluchko Z., Prochno J., Ramanan K.: Large Deviation Principles for Lacunary Sums, Submitted. arXiv:2012.05281.
  47. Desmettre S., Wenzel J.: On the Valuation of Discrete Asian Options in High Volatility Environments, Submitted. Link.

  48. Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti, Paolo Minelli, On the number of gaps of sequences with Poissonian Pair Correlations, Submitted. arXiv:1908.06292.

  49. Wilfried Imrich, Thomas Lachmann, Thomas W. Tucker, Gundelinde M. Wiegel, Asymmetrizing cost and density of vertex-transitive cubicgraphs, Submitted. PDF.

  50. Baci A., Kabluchko K., Prochno J., Sonnleitner M., Thäle Ch.: Limit theorems for random points in a simplex, Submitted. arXiv:2005.04911.

  51. Hinrichs A., Prochno J., Vybiral J.: Gelfand numbers of embeddings of Schatten classes. In: Mathematische Annalen, to appear. arXiv:2011.06554.

  52. Ivanisvili P., Lindenberger A., Müller P. F.X., Schmuckenschläger M.: Hyper contractivity on the unit circle for ultraspherical measures: linear case, Submitted. arXiv:2004.05567.

  53. Krieg D., Sonnleitner M.: Random points are optimal for the approximation of Sobolev functions, Submitted. arXiv:2009.11275.

  54. Ebert A., Kritzer P., Osisiogu O., Stepaniuk T.: Construction of good polynomial lattice rules in weighted Walshspaces by an alternative component-by-component construction, Submitted. arXiv:2101.12586.

  55. Tichy R., Vukusic I., Yang D., Ziegler V.: Integers representable as differences of linear recurrence sequences, Submitted. arXiv:2008.00844.

  56. Ddamulira M., Luca F.: On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. In: Ramanujan J., to appear.

  57. Ddamulira M.: Padovan numbers that are concatenations of two distinct repdigits. In. Math. Slovaca, to appear. arXiv:2003.10705

  58. Ebert A., Pillichshammer F.: Tractability of approximation in the weighted Korobov space in the worst-case setting -- a complete picture. In: J. Complexity, to appear, 2021. arXiv:2102.01449

  59. Kritzinger R., Wiart J.: Improved dispersion bounds for modified Fibonacci lattices. In: J. Complexity, 63, 14 pp., 2021. arXiv:2007.02297.

  60. Kritzinger R.: Dispersion of digital (0,m,2) nets. In: Monatshefte für Mathematik, to appear. arXiv:2004.14760.

  61. Kiuchi I., Saad Eddin S.: On sums of arithmetic functions involving the greatest common divisor, Submitted, 2021. arXiv:2102.03714.

  62. Dick J., Pillichshammer F.: Weighted integration over a hyperrectangle based on digital nets and sequences. In: J. Comput. Appl. Math., to appear. arXiv:2009.06993.

  63. Hofer R., Kaltenböck L.: Pair correlations of Halton and Niederreiter Sequences are not Poissonian, in Monatsheft für Mathematik 194, pp. 789-809, 2021. Link.
  64. Desmettre S., Steffensen M.: Optimal Investment with Uncertain Risk Aversion, Submitted, 2021. Link.
  65. Technau M., Zafeiropoulos A.: Metric results on summatory arithmetic functions on Beatty sets. In: Acta Arith., 197(1), pp. 93 - 104, 2021. arXiv:1907.06050.
  66. Pollington A., Velani S., Zafeiropoulos A., Zorin A.: Inhomogeneous Diophantine Approximation on M0-sets with restricted denominators, Submitted, 2019. arXiv:1906.01151.
  67. Neumüller M.: On the asymptotic behaviour of the sine product $\prod_{r=1}^n |2 \sin(\pi r \alpha )|$, Submitted, 2021. arXiv:2103.14307.
  68. Beltrán C., Etayo U., Marzo J., Ortega-Cerdá J.: A sequence of polynomials with optimal condition number. In: J. Amer. Math. Soc., 34(1), pp. 219-244, 2021. doi:10.1090/jams/956.
  69. Bilyk D., Ferizovic D., Glazyrin A., Matzke R., Park J., Vlasiuk O.: Potential Theory with Multivariate Kernels, Submitted, 2021. arXiv:2104.03410.
  70. Brauchart J.S., Grabner P.J.: Weighted $L^2$-norms of Gegenbauer polynomials. manuscript, 2021. arXiv:2103.08303.
  71. Feigenbaum A.S., Grabner P.J., Hardin D.P.: Eigenfunctions of the Fourier Transform with specified zeros. In: Math. Proc. Cambridge Philos. Soc., to appear, 2021. arXiv:1907.08558.
  72. Ferizovic D.: On the $L^2$-norm of Gegenbauer polynomials. In: Math. Sci., to appear, 2021. arXiv:1909.08121.
  73. Grabner P.J.: Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike. In: Ramanujan J., to appear, 2021. arXiv:2007.13569.
  74. Etayo U.: A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials, Submitted. arXiv:1912.05521.
  75. Etayo U.: Spherical cap discrepancy of the Diamond ensemble, Submitted. arXiv:1910.05140.
  76. Heiny J., Johnston S., Prochno J.: Thin-shell theory for rotationally invariant random simplices, Submitted, 2021. arXiv:2103.11872.
  77. Breneis S., Prochno J., Rudolf D.: The minimal spherical dispersion, Submitted, 2021. arXiv:2103.11701.
  78. Johnston S., Kabluchko Z., Prochno J.: Projections of the uniform distribution on the cube - a large deviation perspective, Submitted, 2021. arXiv:2103.16430.
  79. Prochno J., Strzelecki M.: Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, Submitted, 2021. arXiv:2103.13050.
  80. Gómez A.-I., Gómez-Pérez D., and Pillichshammer F.: Secure pseudorandom bit generators and point sets with low star-discrepancy. In: J. Comput. Appl. Math., to appear. arXiv:2004.14158.
  81. Lemieux Ch. and Wiart J.: On the distribution of scrambled (0,m,s)-nets over unanchored boxes. Submitted, 2021.

Publications in the period 01.01.2020-31.12.2020: PDF

Publications in the period 01.01.2019-31.12.2019: PDF

Publications in the period 01.01.2018-31.12.2018: PDF

Publications in the period 01.01.2017-31.12.2017: PDF

Publications in the period 01.01.2016-31.12.2016: PDF

Publications in the period 01.01.2015-31.12.2015: PDF

Publications in the period 01.02.2014-31.12.2014: PDF

Books in the period 01.01.2019 until today:

  1. Hickernell, F.J, Kritzer, P. (eds.): Multivariate Algorithms and Information-Based Complexity. DeGruyter, Berlin/Boston, 2020. Link
  2. Dick J., Bilyk D., and Pillichshammer F. (eds.): Discrepancy Theory, De Gruyter, Berlin, 2020. ISBN: 978-3-11-065115-7
  3. Larcher G.: Quantitative Finance: Strategien, Investments, Analysen. Springer-Gabler-Verlag, 2020. ISBN: 978-3-658-29157-0


Books in the period 01.02.2014-31.01.2018:

  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 01.02.2018 until today:

  • Stefan Kremsner: Numerical analysis of backward stochastic differential equations. In Progress. (Supervisor: Gunther Leobacher)
  • Mathias Sonnleitner: The power of random information on the sphere. In progress. (Supervisor: Aicke Hinrichs)
  • Onyekachi Osisiogu: Rank-1 Lattices: Theory, Constructions, and Applications. In progress (Supervisor: Peter Kritzer)
  • Alexander Lindenberger: Reproducing Kernels and Applications to Numerical Problems - Beyond Hilbert Spaces. In progress. (Supervisor: Aicke Hinrichs)
  • Damir Ferizović: Uniform Point Distributions and Energy Estimates on Compact Riemannian Manifolds. 2021. (Supervisor: Peter Grabner)
  • Mahadi Ddamulira: Diophantine Equations and Linearly Recurrent Sequences. 2020. (Supervisor: Robert Tichy) Link
  • Johann Verwee: Effective Erdös-Wintner Theorem. 2020. (Supervisor: Michael Drmota and Gerald Tenenbaum)
  • Lisa Kaltenböck: On distribution properties of sequences in the unit cube. 2020. (Supervisor: Gerhard Larcher)
  • Mario Neumüller: Two Contemporary Issues in Number Theory: Sequences with Low Star Discrepancy and the Asymptotic Behaviour of the Sudler Product. 2019. (Supervisor: Friedrich Pillichshammer) PDF
  • Johannes Fürst: An Empirical Investigation on Fast and Stable Methods for the Calibration of Financial Models. In progress. (Supervisor: Gunther Leobacher)

PhD Theses in the period 01.02.2014-31.01.2018:

  • K.C. Chim: Linear forms in logarithms and applications to Diophantine problems. 2018. (Supervisor: Robert Tichy)
  • Ida Aichinger: Distribution Properties of Particle Movements. 2017. (Supervisor: Gerhard Larcher) PDF
  • Ralph Kritzinger: Point sets and sequences with the optimal order of $L_p$ 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.
  • Markus Hittmeir: On the Complexity of Integer Factorization and Related Problems. 2017. (Supervisor: Peter Hellekalek)
  • Alexander Bors: On Dynamical Aspects of Finite Group Endomorphisms. 2016. (Supervisor: Peter Hellekalek)
  • Michaela Szölgyenyi: Dividend Maximization in Hidden Markov Models and Analysis of Associated Stochastic Differential Equations. 2015. (Supervisor: Gunther Leobacher and Stefan Thonhauser) Link.