Publications/Preprints

Below are some articles that you might find interesting. You can take a look at some of the abstracts before downloading the files.
  1. P. Kurlberg, Z. Rudnick. The distribution of spacings between quadratic residues. Duke Math. J., 100(2):211-242, 1999. MR1722952.
  2. D. Bump, K.K.S. Choi, P. Kurlberg, J. Vaaler. A local Riemann hypothesis. I. Math. Z., 233(1):1-19, 2000. MR1738342.
  3. P. Kurlberg. A local Riemann hypothesis. II. Math. Z., 233(1):21-37, 2000. MR1738343.
  4. P. Kurlberg. The distribution of spacings between quadratic residues. II. Israel J. Math., 120(A):205-224, 2000. MR1815376.
  5. P. Kurlberg, Z. Rudnick. Hecke theory and equidistribution for the quantization of linear maps of the torus. Duke Math. J., 103(1):47-77, 2000. MR1758239.
  6. P. Kurlberg, Z. Rudnick. On Quantum Ergodicity for Linear Maps of the Torus. Comm. Math. Phys., 222(1):201-227, 2001. MR1853869.
  7. P. Kurlberg, Z. Rudnick. Value distribution for eigenfunctions of desymmetrized quantum maps. Int. Math. Res. Not., (18):985-1002, 2001. MR1860122.
  8. P. Kurlberg. On a character sum problem of H. Cohn. J. of Number Theory, 92(1):174-181, 2002. MR1880592.
  9. P. Kurlberg. On the order of unimodular matrices modulo integers. Acta Arith., 110(2):141-151, 2003. MR2008081.
  10. P. Kurlberg, Z. Rudnick. On the distribution of matrix elements for the quantum cat map. Annals of Math., 161(1):489-507, 2005. MR2150390.
  11. J. Brzezinski, W. Holsztynski, P. Kurlberg. On the congruence $ax+by\equiv1$ modulo $xy$. Experiment. Math., 14(4):391-401, 2005. MR2193402.
  12. P. Kurlberg, C. Pomerance. On the period of the linear congruential and power generators. Acta Arith, 119(2):149-169, 2005. MR2167719.
  13. L. Fainsilber, P. Kurlberg, B. Wennberg. Lattice points on circles and discrete velocity models for the Boltzmann equation. SIAM J. Math. Anal., 37(6):1903-1922 (electronic), 2006. MR2213399.
  14. L. Fainsilber, P. Kurlberg, B. Wennberg. The Boltzmann equation on a two-dimensional lattice; theoretical and numerical results. Bull. Inst. Math. Acad. Sin. (N.S.), 2(2):667-685, 2007. MR2325732.
  15. P. Kurlberg. Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps. Ann. Henri Poincaré, 8(1):75-89, 2007. MR2299193.
  16. P. Kurlberg, L. Rosenzweig, Z. Rudnick. Matrix elements for the quantum cat map: fluctuations in short windows. Nonlinearity, 20(10):2289-2304, 2007. MR2356110 (2008k:81117).
  17. P. Kurlberg. Bounds on exponential sums over small multiplicative subgroups. In Additive combinatorics, vol. 43 of CRM Proc. Lecture Notes, pages 55-68. Amer. Math. Soc., Providence, RI, 2007. MR2359468 (2009k:11129).
  18. P. Kurlberg, C. Pomerance. Lower bounds on the period of some pseudorandom number generators. In Proceedings of Conference on Algorithmic Number Theory 2007, vol. 46 of TUCS Gen. Pub., pages 74-81. Turku Cent. Comput. Sci., Turku, Finland, 2007.
  19. A. Granville, P. Kurlberg. Poisson statistics via the Chinese remainder theorem. Adv. Math., 218(6):2013-2042, 2008. MR2431668 (2009k:11126).
  20. J.B. Friedlander, P. Kurlberg, I.E. Shparlinski. Products in residue classes. Math. Res. Lett., 15(6):1133-1147, 2008. MR2470390.
  21. P. Kurlberg, Z. Rudnick. The fluctuations in the number of points on a hyperelliptic curve over a finite field. J. Number Theory, 129(3):580-587, 2009. MR2488590.
  22. P. Kurlberg. Poisson spacing statistics for value sets of polynomials. Int. J. Number Theory, 5(3):489-513, 2009. MR2529087.
  23. R.L. Benedetto, D. Ghioca, P. Kurlberg, T.J. Tucker, U. Zannier. The dynamical Mordell-Lang conjecture: the cyclic case. To appear in Mathematische Annalen.
  24. R.L. Benedetto, D. Ghioca, P. Kurlberg, T.J. Tucker. A gap principle for dynamics. Compos. Math., 146(4):1056-1072, 2010. 2660684.
  25. P. Kurlberg, I. Wigman. Gaussian point count statistics for families of curves over a fixed finite field. Int. Math. Res. Not. IMRN, (10):2217-2229, 2011. 2806563.
  26. P. Kurlberg. On Abel prize Laureate John Tate's work. Medlemsutskicket, Svenska matematikersamfundet, May 2010.
  27. P. Kurlberg. Björklunds skola i retorikernas våld. Expressen debatt, 26 Nov 2010.
  28. R.L. Benedetto, D. Ghioca, B. Hutz, P. Kurlberg, T. Scanlon, T.J. Tucker. Periods of rational maps modulo primes. To appear in Math. Annalen.
  29. P. Kurlberg, J.C. Lagarias, C. Pomerance. Product-free sets with high density. To appear in Acta Arith.
  30. P. Kurlberg, C. Pomerance. On a problem of Arnold: the average multiplicative order of a given integer. Submitted.
  31. P. Kurlberg, J.C. Lagarias, C. Pomerance. On the maximal density of product-free sets in $Z/nZ$. To appear in IMRN.
  32. M. Krishnapur, P. Kurlberg, I. Wigman. Nodal length fluctuations for arithmetic random waves. To appear in Annals of Math.
  33. P. Kurlberg, J.C. Lagarias, C. Pomerance. On sets of integers which are both sum-free and product-free. Submitted.
  34. T. Freiberg, P. Kurlberg. On the average exponent of elliptic curves modulo $p$. Submitted.

Links to my coauthors: Robert Benedetto, Juliusz Brzezinski, Daniel Bump, Stephen Choi, Laura Fainsilber, John Friedlander, Dragos Ghioca, Andrew Granville, Benjamin Hutz, Manjunath Krishnapur, Jeffrey Lagarias, Carl Pomerance, Lior Rosenzweig, Zeev Rudnick, Thomas Scanlon, Igor Shparlinski, Thomas Tucker, Jeffrey Vaaler, Bernt Wennberg, Igor Wigman.

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