### Mordechay B. Levin

Email: mlevin@math.biu.ac.il
Phone: +972-3-531-7854
Fax: +972-3-535-3325
Office: Computer and Mathematics Bldg (209), Room 201
Office Hours: Sunday 12:00 to 13:30
Updated Jan 1, 2019

Curs 89-262 (Hebrew)

Curs 88-265 (Hebrew)

Curs 88-373 (Hebrew)

Research Interests

My research interests are number theory, uniform distributed
sequences, limit theorems

Publications

37. On a bounded remainder set for $(t,s)$ sequences I http://arxiv.org/abs/1901.00135, 32 p.

36. On a bounded remainder set for a digital Kronecker sequence http://arxiv.org/abs/1901.00042, 23 p.

35. On the upper bound of the $L_p$ discrepancy of Halton's sequence and the Central Limit Theorem for Hammersley's net http://arxiv.org/abs/1806.11498 , 42 p.

34. On the lower bound of the discrepancy of $(t,s)$-sequences: II Online J. of Analitic Combinatoric 2017, 74 p.

33. On the lower bound of the discrepancy of Halton's sequence II European Journal of Mathematics, 2 (2016) 874–885

32. On the lower bound of the discrepancy of $(t,s)$-sequences: I C. R. Math. Acad. Sci. Paris, 354 (2016), no. 5, 445-448

31. On the lower bound of the discrepancy of Halton's sequence: I C. R. Math. Acad. Sci. Paris, 354 (2016), no. 5, 445-448

30. On Gaussian limiting distribution of lattice points in a parallelepiped Unif. Distrib. Theory 11 (2016), no. 2, 45-89.

29. On the lower bound in the lattice point remainder problem for a parallelepiped Discrete \& Computational Geometry, 54 (2015), no. 4, 826-870

28. A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series Colloq. Mathem. 131 (2013), no. 1, 13-27.

27. Central Limit Theorem for $Z_{+}^d$-actions by toral endomorphisms, Electronic Journal of Probability, 18 (2013), no. 35, 42~pp.

26. On the Statistical Independence of Shift-Register Pseudorandom Multisequence over Part of the Period Unif. Distrib. Theory, 8 (2013), no. 1, 121-133. (with I. Volinsky)

25. Discrepancy estimate of normal vectors (the case of hyperbolic matrices) Unif. Distrib. Theory 5 (2010), no. 2, 141-167. (with I. Volinsky)

24. Adelic constructions of low discrepancy sequences Online J. Anal. Comb. . No. 5 (2010), 27 p.

23. On low discrepancy sequences and low discrepancy ergodic transformations of the multidimensional unit cube Israel J. Math. 178 (2010), 61-106. 178 (2010), 61-106.

22. Discrepancy estimates of normal vectors Unif. Distrib. Theory 3 (2008), no. 1, 19-33. (with I. Volinsky)

21. On polynomially normal lattice configurations Monatsh. Math. 147 (2006), no. 2, 137--153 (with M. Smorodinsky).

20. On linear normal lattices configurations J. Théor. Nombres Bordeaux, 17 (2005), no. 3, 825--858 (with M. Smorodinsky).

19. Explicit construction of normal lattice configurations Colloq. Math. 102 (2005), no. 1, 33--47 (with M. Smorodinsky).

18. Central limit theorems for the ergodic adding machine Israel Journal of Mathem, 2003, v. 134, p. 61-92 (with E. Merzbach)

17. On the discrepancy estimates of normal lattice configuration Journal de Theorie de Nombres Bordeaux, 2001, v. 13, p. 483-527.

16. On the statistical independence of compound pseudorandom numbers over part of the period ACM Trans. Model Comput. Simulation, 2001, v. 11,no. 3, p. 294-311.

15. Explicit digital inversive pseudorandom numbers Math. Slovaca, 2000, v. 50, no. 5, p. 581-598.

14. A $Z^d$ generalisation of Davenport and Erdos theorem on normal numbers Colloq. Mathem., 2000, v. 84/85, p. 431-441 (with M. Smorodinsky)

13. Discrepancy estimates of completely uniformly distributed and pseudo-random number sequences Intern. Math. Res. Notes, 1999, no. 22, pp. 1231 -1251.

12. On the discrepancy estimate of normal numbers Acta Arithmetica, 1999, v. 88, pp. 99-111.

11. On the discrepancy of Markov-normal sequences Journal de Theorie de Nombres Bordeaux, 1997, v.8, pp. 150-165.

10. Simultaneously absolutely normal numbers Mat. Zametki 48 (1990), no. 6, 61-71. English translation in Math. Notes 48 (1990), no. 5-6, 1213-1220 (1991). {\bf MR} 92 g: 11077.

9. Effectivization of the Koksma theorem, Mat. Zametki, 47 (1990), no. 1, 163-166. {\bf MR} 91 i: 11095.

8. The choice of parameters in generators of pseudorandom numbers. Dokl. Akad. Nauk SSSR, 307 (1989), no. 3, 529-534. English translation in Soviet Math. Dokl. 40 (1990), no. 1, 101-103. {\bf MR} 91 d: 11094.

7. Uniform distribution of the matrix exponential function, Investigations in number theory, 42-62, Saratov Gos. Univ. 1988. {\bf MR} 91 d: 11085.

6. On the complete uniform distribution of the fractional part of the exponential function Trudy Sem. Petrovsk. No. 7 (1981), pp. 245-256. English translation in Journal of Soviet Mathematics, 1985, v. 31, pp. 3247-3256.

5. Absolutely normal numbers. Vestnik Moscov. Univ. ser. I, Mat-Meh, 1979, no. 1, 31-37, 87. English translation in Moscow Univ. Math. Bull., 34 (1979), no. 1, 32-39. {\bf MR} 80d: 10076.

4. Uniform distribution of fractional part of recurrent sequences Uspechi Mat. Nauk, 34 (1979), no. 3 (207), 203-204. English translation in Russian Math. Surveys, 34:3 (1979), 207-208. (with Sparlinskii I.E.)

3. The uniform distribution of the sequence $\{\lambda ^n \}$., Uspechi Mat. Nauk, 32 (1977), no. 4, 246-247.

2. The distribution of fractional parts of the exponential function Izv. Viss. Ucebn. Zaved. Mathematika, 1977, no. 11 (186), 50-57. English translation in Soviet Math. (Iz.Vuz) 21 (1977), no. 11, 41-47

1. The uniform distribution of the sequence $\{\alpha \lambda ^n \}$ Mat.sb. 98 (140), 1975, no. 2 (10), 207-222, 333. English translation in Math. USSR Sbornik, 1975, v. 27, pp. 183-197

PhD students I. Volinskay (graduated in 2011)