# 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. (Alternatively, most articles can be found on the arxiv, or at google scholar.)
1. P. Kurlberg. A Local Riemann Hypothesis. PhD thesis, Stanford University, 1997.
2. P. Kurlberg, Z. Rudnick. The distribution of spacings between quadratic residues. Duke Math. J., 100(2):211-242, 1999. MR1722952.
3. D. Bump, K.K.S. Choi, P. Kurlberg, J. Vaaler. A local Riemann hypothesis. I. Math. Z., 233(1):1-19, 2000. MR1738342.
4. P. Kurlberg. A local Riemann hypothesis. II. Math. Z., 233(1):21-37, 2000. MR1738343.
5. P. Kurlberg. The distribution of spacings between quadratic residues. II. Israel J. Math., 120(A):205-224, 2000. MR1815376.
6. 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.
7. P. Kurlberg, Z. Rudnick. On Quantum Ergodicity for Linear Maps of the Torus. Comm. Math. Phys., 222(1):201-227, 2001. MR1853869.
8. P. Kurlberg, Z. Rudnick. Value distribution for eigenfunctions of desymmetrized quantum maps. Int. Math. Res. Not., (18):985-1002, 2001. MR1860122.
9. P. Kurlberg. On a character sum problem of H. Cohn. J. of Number Theory, 92(1):174-181, 2002. MR1880592.
10. P. Kurlberg. On the order of unimodular matrices modulo integers. Acta Arith., 110(2):141-151, 2003. MR2008081.
11. P. Kurlberg, Z. Rudnick. On the distribution of matrix elements for the quantum cat map. Annals of Math., 161(1):489-507, 2005. MR2150390.
12. J. Brzezinski, W. Holsztynski, P. Kurlberg. On the congruence $ax+by\equiv1$ modulo $xy$. Experiment. Math., 14(4):391-401, 2005. MR2193402.
13. P. Kurlberg, C. Pomerance. On the period of the linear congruential and power generators. Acta Arith, 119(2):149-169, 2005. MR2167719.
14. 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.
15. 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.
16. P. Kurlberg. Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps. Ann. Henri Poincaré, 8(1):75-89, 2007. MR2299193.
17. 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).
18. 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).
19. 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.
20. A. Granville, P. Kurlberg. Poisson statistics via the Chinese remainder theorem. Adv. Math., 218(6):2013-2042, 2008. MR2431668 (2009k:11126).
21. J.B. Friedlander, P. Kurlberg, I.E. Shparlinski. Products in residue classes. Math. Res. Lett., 15(6):1133-1147, 2008. MR2470390.
22. 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.
23. P. Kurlberg. Poisson spacing statistics for value sets of polynomials. Int. J. Number Theory, 5(3):489-513, 2009. MR2529087.
24. R.L. Benedetto, D. Ghioca, P. Kurlberg, T.J. Tucker. A gap principle for dynamics. Compos. Math., 146(4):1056-1072, 2010. MR2660684.
25. P. Kurlberg. On Abel prize Laureate John Tate's work. Medlemsutskicket, Svenska matematikersamfundet, May 2010.
26. P. Kurlberg. Björklunds skola i retorikernas våld. Expressen debatt, 26 Nov 2010.
27. 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. MR2806563.
28. R.L. Benedetto, D. Ghioca, P. Kurlberg, T.J. Tucker. A case of the dynamical Mordell-Lang conjecture. Math. Ann., 352(1):1-26, 2012. MR2885573.
29. P. Kurlberg, J.C. Lagarias, C. Pomerance. Product-free sets with high density. Acta Arith., 155(2):163-173, 2012. MR2981989.
30. P. Kurlberg, J.C. Lagarias, C. Pomerance. On sets of integers which are both sum-free and product-free. Integers, 12B(Proceedings of the Integers Conference 2011):Paper No. A4, 9, 2012/13. MR3055678.
31. R.L. Benedetto, D. Ghioca, B. Hutz, P. Kurlberg, T. Scanlon, T.J. Tucker. Periods of rational maps modulo primes. Math. Ann., 355(2):637-660, 2013. MR3010142.
32. P. Kurlberg, C. Pomerance. On a problem of Arnold: The average multiplicative order of a given integer. Algebra and Number Theory, 7(4):981-999, 2013. MR3095233.
33. P. Kurlberg, J.C. Lagarias, C. Pomerance. The maximal density of product-free sets in $\mathbb Z/n\mathbb Z$. Int. Math. Res. Not. IMRN, (4):827-845, 2013. MR3024266.
34. M. Krishnapur, P. Kurlberg, I. Wigman. Nodal length fluctuations for arithmetic random waves. Ann. of Math. (2), 177(2):699-737, 2013. MR3010810.
35. T. Freiberg, P. Kurlberg. On the average exponent of elliptic curves modulo $p$. Int. Math. Res. Not. IMRN, (8):2265-2293, 2014. MR3194018.
36. P. Kurlberg, H. Ueberschär. Quantum Ergodicity for Point Scatterers on Arithmetic Tori. Geom. Funct. Anal., 24(5):1565-1590, 2014. MR3261634.
37. P. Kurlberg, F. Luca, I.E. Shparlinski. On the fixed points of the map $x \mapsto x^x$ modulo a prime. Math. Res. Lett., 22(1):141-168, 2015. MR3342182.
38. E. Amerik, P. Kurlberg, K.D. Nguyen, A. Towsley, B. Viray, J.F. Voloch. Evidence for the Dynamical Brauer-Manin Criterion. Exp. Math., 25(1):54-65, 2016. MR3424832.
39. P. Kurlberg, I. Wigman. Non-universality of the Nazarov-Sodin constant. C. R. Math. Acad. Sci. Paris, 353(2):101-104, 2015. MR3300938.
40. J. Juul, P. Kurlberg, K. Madhu, T.J. Tucker. Wreath products and proportions of periodic points. Int. Math. Res. Not. IMRN, (13):3944-3969, 2016. MR3544625.
41. P. Kurlberg, H. Ueberschär. Superscars in the Seba billiard. J. Eur. Math. Soc. (JEMS), 19(10):2947-2964, 2017.
42. P. Kurlberg, I. Wigman. On probability measures arising from lattice points on circles. Math. Ann., 367(3-4):1057-1098, 2017. MR3623219.
43. P. Kurlberg, L. Rosenzweig. Superscars for Arithmetic Toral Point Scatterers. Comm. Math. Phys., 349(1):329-360, 2017. MR3592751.
44. S. Holmin, N. Jones, P. Kurlberg, C. McLeman, K. Petersen. Missing class groups and class number statistics for imaginary quadratic fields. Exp. Math., 28(2):233-254, 2019. MR3955814.
45. S. Holmin, P. Kurlberg, D. Månsson. On the free path length distribution for linear motion in an $n$-dimensional box. J. Phys. A, 51(46):465201, 23, 2018. MR3876700.
46. A.T. Felix, P. Kurlberg. On the fixed points of the map $x\mapsto x^x$ modulo a prime, II. Finite Fields Appl., 48:141-159, 2017. MR3705740.
47. T. Freiberg, P. Kurlberg, L. Rosenzweig. Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers. Commun. Number Theory Phys., 11(4):837-877, 2017. MR3733767.
48. P. Kurlberg. Level repulsion for arithmetic toral point scatterers in dimension $3$. Submitted.
49. P. Kurlberg, I. Wigman. Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves. Adv. Math., 330:516-552, 2018. MR3787552.
50. P. Kurlberg, L. Rosenzweig. Prime and M\"obius correlations for very short intervals in $\mathbb F_q[x]$. Submitted.
51. R. de la Bretèche, P. Kurlberg, I. Shparlinski. On the number of products which form perfect powers and discriminants of multiquadratic extensions. IMRN, 2019.
52. P. Kurlberg, L. Rosenzweig. The Chebotarev density theorem for function fields -- incomplete intervals. Finite Fields and Their Applications, to appear.
53. O. Klurman, P. Kurlberg. A note on multiplicative automatic sequences. C. R. Math. Acad. Sci. Paris, 357(10):752-755, 2019. MR4031444.
54. O. Klurman, P. Kurlberg. A note on multiplicative automatic sequences, II. Bull. Lond. Math. Soc., 52(1):185-188, 2020. MR4072043.
55. P. Kurlberg, H. Ueberschär. Non-gaussian waves in Seba's billiard. Submitted.
56. P. Kurlberg, S. Lester, L. Rosenzweig. Superscars for Arithmetic Toral Point Scatterers II. Submitted.
57. P. Kurlberg, I. Wigman, N. Yesha. The defect of toral Laplace eigenfunctions and Arithmetic Random Waves. Submitted.
58. D. Chatzakos, P. Kurlberg, S. Lester, I. Wigman. On the distribution of lattice points on hyperbolic circles. Algebra and Number Theory, to appear.
59. P. Kurlberg, G. Zickert. Formal uniqueness in Ewald sphere corrected single particle analysis. Preprint.

Remark: The article "Localised semiclassical measures for point scatterers on diophantine tori" (e.g., it was cited in [36] under this name) appeared in JEMS with the title "Superscars in the Seba billiard" (see [41] above.)