Publications

  1. P. J. Grabner: On digit expansions with respect to second order linear recurring sequences, in E. Hlawka and R. F. Tichy, eds., Number Theoretic Analysis, no. 1452 in Lecture Notes in Math., pp. 58--64, Springer (1990).

  2. P. J. Grabner and R. F. Tichy: Contributions to digit expansions with respect to linear recurrences, J. Number Th., 36, (1990), 160--169.

  3. P. J. Grabner and R. F. Tichy: Remark on an inequality of Erdös-Turán-Koksma, Anz. Österr. Akad. Wiss., 127, (1990), 15--22.

  4. P. J. Grabner: Eine stetige nirgends differenzierbare Funktion in der Zahlentheorie, Wurzel, Zeitschrift für Mathematik, Universität Jena, 6.

  5. P. J. Grabner: Erdös-Turán type discrepancy bounds, Monatsh. Math., 111, (1991), 127--135.

  6. P. J. Grabner: Ziffernentwicklungen bezüglich linearer Rekursionen, österr. Akad. Wiss. SB II, 199, (1991), 1--21.

  7. P. J. Grabner and R. F. Tichy: Α-expansions, linear recurrences and the sum-of-digits function, Manuscr. Math., 70, (1991), 311--324.

  8. P. J. Grabner: Block distributions in random strings, Ann. Inst. Fourier, 43, (1993), 539--549.

  9. P. J. Grabner: Completely q-multiplicative functions: the Mellin-transform approach, Acta Arith., 65, (1993), 85--96.

  10. P. J. Grabner: Metric results on a new notion of discrepancy, Math. Slovaca, 42, (1993), 615--619.

  11. P. J. Grabner: A note on the parity of the sum-of-digits function, Actes Séminaires Lotharingien de Combinatoires, 30, (1993), 35--42.

  12. P. J. Grabner: Searching for losers, Random Structures and Algorithms, 4, (1993), 99--110.

  13. P. J. Grabner, P. Kirschenhofer, H. Prodinger, and R. F. Tichy: On the moments of the sum-of-digits function, in G. Bergum, ed., Applications of Fibonacci Numbers, vol. 5, pp. 263--271, Kluwer (1993).

  14. P. J. Grabner, H. Prodinger, and R. F. Tichy: Asymptotic analysis of a class of functional equations and applications, Séminaire de Théorie des Nombres, Bordeaux, 5, (1993), 365--381.

  15. P. J. Grabner and R. F. Tichy: Spherical designs, discrepancy and numerical integration, Math. Comp., 60, (1993), 327--336.

  16. P. J. Grabner, R. F. Tichy, and R. Winkler: On the stability of the quotients of successive terms of linear recurring sequences, in A. van~der Poorten, I. Shparlinski, and H. Zimmer, eds., Number Theoretic and Algebraic Methods in Computer Science, pp. 185--192, World Scientific, Moscow (1993).

  17. P. Flajolet, P. J. Grabner, P. Kirschenhofer, H. Prodinger, and R. F. Tichy: Mellin transforms and asymptotics: digital sums, Theor. Comput. Sci., 123, (1994), 291--314.

  18. P. J. Grabner, P. Kiss, and R. F. Tichy: Diophantine approximation in terms of linear recurring sequences, in K. Dilcher, ed., Proceedings of the Fourth Conference of the Canadian Number Theory Association, vol. 15 of CMS Conference Proceedings, pp. 187--195, Amer. Math. Soc. (1994).

  19. P. J. Grabner, I. Nemes, A. Pethö, and R. F. Tichy: Generalized Zeckendorf expansions, Appl. Math. Letters, 7 (2), (1994), 25--28, corrigendum: 7,no. 6:25--26, 1994.

  20. P. J. Grabner, A. Pethö, R. F. Tichy, and G. J. Wöginger: Associativity of recurrence multiplication, Appl. Math. Letters, 7, (1994), 85--90.

  21. P. J. Grabner and H. Prodinger: The Fibonacci killer, Fibonacci Q., 32, (1994), 389--394.

  22. P. J. Grabner and R. F. Tichy: Remarks on statistical independence, Math. Slovaca, 44, (1994), 91--94.

  23. C. Biester, P. J. Grabner, G. Larcher, and R. F. Tichy: Adaptive search in quasi-Monte Carlo optimization, Math. Comp., 64, (1995), 807--818.

  24. P. Flajolet, P. J. Grabner, P. Kirschenhofer, and H. Prodinger: On Ramanujan's Q-function, J. Comput. Appl. Math., 58, (1995), 103--116.

  25. P. J. Grabner, P. Liardet, and R. F. Tichy: Odometers and systems of numeration, Acta Arith., 70, (1995), 103--123.

  26. G. Barat and P. J. Grabner: Distribution properties of G-additive functions, J. Number Th., 60, (1996), 103--123.

  27. D. Barbolosi and P. J. Grabner: Distribution des coefficients multinomiaux et q-binomiaux modulo p, Indag. Math., 7, (1996), 129--135.

  28. P. J. Grabner, I. Nemes, A. Pethö, and R. F. Tichy: On the least significant digit of Zeckendorf expansion, Fibonacci Q., 34, (1996), 147--151.

  29. P. J. Grabner and H. Prodinger: Asymptotic analysis of the moments of the Cantor distribution, Stat. Probab. Letters, 26, (1996), 243--248.

  30. P. J. Grabner and H. Prodinger: On the optimality of an algorithm of Reingold and Supowit, J. Autom. Lang. Comb., 1, (1996), 5--11.

  31. P. J. Grabner and J. M. Thuswaldner: Analytic continuation of a class of Dirichlet series, Abh. Math. Semin. Hamburg, 66, (1996), 281--287.

  32. P. J. Grabner, R. F. Tichy, and U. T. Zimmermann: Inequalities for the Gamma-function with applications to permanents, Discr. Math., 154, (1996), 53--62.

  33. P. J. Grabner: Functional iterations and stopping times for Brownian motion on the Sierpinski gasket, Mathematika, 44, (1997), 374--400.

  34. P. J. Grabner, T. Herendi, and R. F. Tichy: Fractal digital sums and codes, Appl. Algebra Eng. Commun. Comput., 8, (1997), 33--39.

  35. P. J. Grabner, B. Klinger, and R. F. Tichy: Discrepancies of point sequences on the sphere and numerical integration, in W. Haußmann, K. Jetter, and M. Reimer, eds., Multivariate Approximation, Recent Trends and Results, Proc. of the 2nd International Conference on Multivariate Approximation Theory, Witten-Bommerholz, pp. 95--112, Akademie Verlag, Berlin (1997).

  36. P. J. Grabner and H. Prodinger: Maximum statistics of N random variables distributed by the negative binomial distribution, Combin. Probab. Comput., 6, (1997), 179--183.

  37. P. J. Grabner, O. Strauch, and R. F. Tichy: Maldistribution in higher dimensions, Math. Pannonica, 8, (1997), 215--223.

  38. P. J. Grabner and W. Woess: Functional iterations and periodic oscillations for the simple random walk on the Sierpinski graph, Stochastic Processes Appl., 69, (1997), 127--138.

  39. P. J. Grabner, P. Kirschenhofer, and H. Prodinger: The sum-of-digits function for complex bases, J. London Math. Soc., 57, (1998), 20--40.

  40. P. J. Grabner and A. Knopfmacher: Metric properties of Engel series expansions of Laurent series, Math. Slovaca, 48, (1998), 233--243.

  41. P. J. Grabner and H. Prodinger: An Asymptotic Study of a Recursion Occurring in the Analysis of an Algorithm on Broadcast Communication, Inf. Process. Lett., 65, (1998), 89--93.

  42. P. J. Grabner and R. F. Tichy: Equidistribution and Brownian motion on the Sierpinski gasket, Monatsh. Math., 125, (1998), 147--164.

  43. J. M. Dumont, P. J. Grabner, and A. Thomas: Distribution of the digits in the expansions of rational integers in algebraic bases, Acta Sci. Math. (Szeged), 65, (1999), 469--492.

  44. P. J. Grabner and P. Liardet: Harmonic properties of the sum-of-digits function for complex bases, Acta Arith., 91, (1999), 329--349.

  45. P. J. Grabner, P. Liardet, and R. F. Tichy: Average case analysis of numerical integration, in W. Haußmann, K. Jetter, and M. Reimer, eds., Advances in multivariate approximation (Witten-Bommerholz, 1998), pp. 185--200, Wiley-VCH, Berlin (1999).

  46. P. J. Grabner, O. Strauch, and R. F. Tichy: L^p-discrepancy and statistical independence of sequences, Czech. Math. J., 49, (1999), 97--110.

  47. P. J. Grabner and J. M. Thuswaldner: On the sum of digits function for number systems with negative bases, Ramanujan J., 4, (2000), 201--220.

  48. G. Barat and P. J. Grabner: Digital functions and distribution of binomial coefficients, J. London Math. Soc., 64, (2001), 523--547.

  49. P. J. Grabner, P. Kirschenhofer, and R. F. Tichy: Combinatorial and arithmetical properties of linear numeration systems, Combinatorica, 22, (2002), 245--267.

  50. P. J. Grabner and H. Prodinger: Some identities for Chebyshev polynomials, Port. Math. (N.S.), 59, (2002), 311--314.

  51. P. J. Grabner and H. Prodinger: Sorting algorithms for broadcast communications: Mathematical analysis, Theor. Comput. Sci., 289, (2002), 51--67.

  52. S. B. Damelin and P. J. Grabner: Energy functionals, numerical integration and asymptotic equidistribution on the sphere, J. Complexity, 19, (2003), 231--246, corrigendum, 20 (2004), 883--884.

  53. P. J. Grabner, C. Heuberger, and H. Prodinger: Subblock occurrences in signed digit representations, Glasg. Math. J., 45, (2003), 427--440.

  54. P. J. Grabner and A. Knopfmacher: Arithmetic and metric properties of p-adic Engel series expansions, Publ. Math. Debrecen, 63, (2003), 363--377.

  55. P. J. Grabner, A. Knopfmacher, and H. Prodinger: Combinatorics of geometrically distributed random variables: run statistics, Theor. Comput. Sci., 297, (2003), 261--270.

  56. P. J. Grabner and M. Rigo: Additive functions with respect to numeration systems on regular languages, Monatsh. Math., 139, (2003), 205--219.

  57. P. J. Grabner and W. Woess, eds.: Proceedings of the conference ``Fractals in Graz 2001'', Trends in Mathematics, Birkhäuser, Basel (2003).

  58. P. J. Grabner: Minima of digital functions related to large digits in Q-adic expansions, Quaest. Math., 27, (2004), 75--87.

  59. P. J. Grabner, C. Heuberger, and H. Prodinger: Distribution results for low-weight binary representations for pairs of integers, Theor. Comput. Sci., 319, (2004), 307--331.

  60. P. J. Grabner, C. Heuberger, and H. Prodinger: Counting optimal joint digit expansions, Integers, 5 (3), (2005), A09, 19 pages (electronic).

  61. P. J. Grabner, C. Heuberger, H. Prodinger, and J. Thuswaldner: Analysis of linear combination algorithms in cryptography, Transactions on Algorithms, 1, (2005), 123--142.

  62. P. J. Grabner and H.-K. Hwang: Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence, Constructive Approximation, 21, (2005), 149--179.

  63. P. J. Grabner, P. Liardet, and R. F. Tichy: Spectral Disjointness of Dynamical Systems Related to Some Arithmetic Functions, Publ. Math. Debrecen, 66, (2005), 213--244.

  64. P. J. Grabner and B. Steinsky: Asymptotic Behaviour of the Poles of a Special Generating Function for Acyclic Digraphs, Aequationes Math., 70, (2005), 268--278.

  65. P. J. Grabner and C. Heuberger: On the number of optimal base 2 representations of integers, Des. Codes Cryptogr., 40, (2006), 25--39.

  66. P. J. Grabner and A. Knopfmacher: Analysis of some new partition statistics, Ramanujan J., 12, (2006), 439--454.

  67. H.-J. Albrecher, M. Drmota, M. Goldstern, P. J. Grabner, and R. Winkler: Robert F. Tichy: 50 Years --- The unreasonable effectiveness of a number theorist, Unif. Distrib. Theory, 2, (2007), 151--160.

  68. G. Derfel, P. J. Grabner, and F. Vogl: Asymptotics of the Poincaré functions, in D. Dawson, V. Jaksic, and B. Vainberg, eds., Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, vol. 42 of CRM Proceedings and Lecture Notes, pp. 113--130, Centre de Recherches Mathématiques, Montreal (2007).

  69. P. Grabner and H. Prodinger: Secant and cosecant sums and Bernoulli-Nörlund polynomials, Quaest. Math., 30, (2007), 159--165.

  70. P. J. Grabner and M. Rigo: Distribution of additive functions with respect to numeration systems on regular languages, Theory Comput. Syst., 40, (2007), 205--223.

  71. P. J. Grabner (reporter): Geometric Measure Theoretic Approaches to Potentials on Fractals and Manifolds, Oberwolfach Rep., 4 (2), (2007), 1027--1072, abstracts from the mini-workhop held April 8--14, 2007, Organized by Peter Grabner, Douglas Hardin, Edward Saff, Martina Zähle.

  72. V. Metz and P. J. Grabner: An interface problem for a Sierpinski and a Vicsek fractal, Math. Nachr., 280, (2007), 1577--1594.

  73. G. Barat and P. J. Grabner: Limit distribution of Q-additive functions from an ergodic point of view, Ann. Univ. Sci. Budapest. Sect. Comput., 28, (2008), 55--78.

  74. G. Derfel, P. J. Grabner, and F. Vogl: Complex asymptotics of Poincaré functions and properties of Julia sets, Math. Proc. Cambridge Philos. Soc., 145, (2008), 699--718.

  75. G. Derfel, P. J. Grabner, and F. Vogl: The Zeta function of the Laplacian on certain fractals, Trans. Amer. Math. Soc., 360, (2008), 881--897.

  76. M. Drmota, P. J. Grabner, and P. Liardet: Block Additive Functions on the Gaussian Integers, Acta Arith., 135, (2008), 299--332.

  77. P. J. Grabner and H. Prodinger: On a constant arising in the analysis of bit comparisons in quickselect, Quaest. Math., 31, (2008), 303--306.

  78. M. Drmota and P. J. Grabner: Analysis of digital functions and applications, in V. Berthé and M. Rigo, eds., Combinatorics, Automata and Number Theory, Encyclopedia of mathematics and its applications, pp. 452--504, Cambridge University Press (2010).

  79. P. J. Grabner and W. Steiner: Redundancy of minimal weight expansions in Pisot bases, Theor. Comput. Sci, 412, (2011), 6303--6315.

  80. G. Derfel, P. J. Grabner, and F. Vogl: Laplace Operators on Fractals and Related Functional Equations, J. Phys. A, 45(46), (2012), 463001 (34 pages) © IOP Publishing

  81. P. J. Grabner, P. Hellekalek, and P. Liardet: The dynamical point of view of low-discrepancy sequences, Unif. Distrib. Theory, 7, (2012), 11--70.

  82. P. J. Grabner and H. Prodinger: Additive irreducibles in α-expansions, Publ. Math. Debrecen, 80, (2012), 405--415.

  83. P. J. Grabner, A. Knopfmacher, and S. G. Wagner: A general asymptotic scheme for moments of partition statistics, Combin. Probab. Comput. 23 (Special Issue 06), (2014), 1057--1086. FirstView, © Cambridge University Press.

  84. P. J. Grabner, Point sets of minimal energy. In Applications of Algebra and Number Theory (Lectures on the Occasion of Harald Niederreiter's 70th Birthday) (edited by G. Larcher, F. Pillichshammer, A. Winterhof, and C. Xing). pp. 109--125, Cambridge University Press (2014).

  85. G. Barat and P. J. Grabner, Combinatorial and probabilistic properties of systems of numeration, Ergodic Theory Dynam. Systems, 36 (2016), 422-457 FirstView , © Cambridge University Press

  86. J. S. Brauchart and P. J. Grabner: Distributing many points on spheres: minimal energy and designs J. Complexity, 31, (2015), 293-326.

  87. P. J. Grabner, Poincaré functional equations, harmonic measures on Julia sets, and fractal zeta functions, . In Fractal Geometry and Stochastics V (edited by C. Bandt, K. Falconer, and M. Zähle), vol. 70 of Progress in Probability. Birkhäuser Verlag, Basel, pp. 157--174. Papers from the conference held in Tabarz, March 24--28, 2014.

  88. G. Barat, P. J. Grabner, and P. Hellekalek, Pierre Liardet (1943--2014) In Memoriam, . Eur. Math. Soc. Newsl., 97, (2015), 52--58.

  89. G. Barat and P. J. Grabner, Spatial equidistribution of binomial coefficients modulo prime powers, , Unif. Distr. Theory, 11, (2016), 151-161.

  90. G. Derfel, P. J. Grabner, and R. F. Tichy, , On the asymptotic behaviour of the zeros of solutions of one functional-differential equation with rescaling, . In Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations (edited by D. Alpay and B. Kirstein), vol. 263 of Operator Theory: Advances and Applications. Springer (2018). pp. 281--293.

  91. P. J. Grabner, A note on some approximation kernels on the sphere. In Contemporary Computational Mathematics - A celebration of the 80th birthday of Ian Sloan (edited by J. Dick, F. Kuo, and H. Wozniakowski). Springer Verlag (2018). pp. 443--454.

  92. J. S. Brauchart, P. J. Grabner, and W. B. Kusner, Hyperuniform point sets on the sphere: deterministic aspects. Constr. Approx., (2019), 45--61.

  93. P. J. Grabner and T. A. Stepanyuk, Comparison of probabilistic and deterministic point sets, . J. Approx. Theory, 239 (2019), 128–143.

  94. P. J. Grabner and T. A. Stepanyuk, Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension, . J. Complexity. 53 (2019), 113-132.

  95. J. S. Brauchart, P. J. Grabner, W. B. Kusner, and J. Ziefle, Hyperuniform point sets on the sphere: probabilistic aspects, Monatsh. Math., 192 (2020), 763--781.

  96. P. J. Grabner, Quasimodular forms as solutions of modular differential equations, . Int. J. Number Theory, 16 (2020), 2233 - 2274, available at ArXiv.

  97. A. S. Feigenbaum, P. J. Grabner, and D. P. Hardin, Eigenfunctions of the Fourier Transform with specified zeros, Math. Proc. Cambridge Philos. Soc. 171 (2021), 329-367. ArXiv

  98. P. J. Grabner, Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike , Ramanujan J., 57, (2022), 1021--1041.

  99. P. J. Grabner, Purity results for some arithmetically defined measures , Indag. Math., (2022), 1033--1048. ArXiv.

  100. A. Anderson, M. Dostert, P. J. Grabner, R. W. Matzke, and T. A. Stepaniuk, Riesz and Green energy on projective spaces. Trans. Amer. Math. Soc. Series B, (2023), 1039--1076. doi:10.1090/btran/161. ArXiv.

  101. B. Borda, P. J. Grabner, and R. W. Matzke, Riesz energy, L2-discrepancy, and optimal transport of determinantal point processes on the sphere and the flat torus (2024). Mathematika, 70, e12245 ArXiv.

  102. J. S. Brauchart, P. J. Grabner, I. H. Sloan, and R. S. Womersley, {N}eedlets liberated. Appl. Comput. Harmon. Anal., (2024), 101693. doi:10.1016/j.acha.2024.101693. ArXiv

  103. J. S. Brauchart and P. J. Grabner, Hyperuniform point sets on projective spaces (2024). ArXiv.

  104. D. Bilyk and P. J. Grabner, Positive definite singular kernels on two-point homogeneous spaces (2024). ArXiv.