### Mordechay B. Levin

Email: mlevin@math.biu.ac.il
Phone: +972-3-531-7854
Fax: +972-3-535-3325
Office: Computer and Mathematics Bldg (216), Room 203
Office Hours: Wendsday 12:00 to 13:30
Updated Jan 1, 2015

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

Selected Publications

1975-1990

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. {\bf MR} 53 10732

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. {\bf MR} 58 21963

3. The uniform distribution of the sequence $\{\lambda ^n \}$., Uspechi Mat.

Nauk, 32 (1977), no. 4, 246-247.

4. Uniform distribution of fractional part of recurrent

sequences (with Sparlinskii I.E.), Uspechi Mat. Nauk, 34

(1979), no. 3 (207), 203-204. English translation in Russian

Math. Surveys, 34:3 (1979), 207-208. {\bf MR} 80 k: 10046

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.

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. {\bf MR} 83 j: 10059.

7. Uniform distribution of the matrix exponential function,

Investigations in number theory, 42-62, Saratov Gos. Univ.

1988. {\bf MR} 91 d: 11085.

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.

9. Effectivization of the Koksma theorem, Mat. Zametki, 47

(1990), no. 1, 163-166. {\bf MR} 91 i: 11095.

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.

1997-

11. On the discrepancy of Markov-normal sequence, Journal

de Theorie de Nombres Bordeaux, 1997, v.8, pp. 150-165.

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12. On the discrepancy estimate of normal numbers,

Acta Arithmetica, 1999, v. 88, pp. 99-111.

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13. Discrepancy estimates of completely uniformly distributed and

pseudo-random number sequences, Intern. Math. Res. Notes, 1999, no. 22,

pp. 1231 -1251.

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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)

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15. Explicit digital inversive pseudorandom numbers, Math. Slovaca,

2000, v. 50, no. 5, p. 581-598.

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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.

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17. On the discrepancy estimates of normal lattice configuration

and jointly normal numbers, Journal de Theorie de Nombres Bordeaux,

2001, v. 13, p. 483-527.

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18. Central limit theorems for the ergodic

adding machine, Israel Journal of Mathem, 2003, v. 134, p. 61-92.

(with E. Merzbach)

19. Explicit construction of normal lattice configurations. Colloq. Math.

102 (2005), no. 1, 33--47 (with M. Smorodinsky).

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20. On linear normal lattices configurations. J. Théor. Nombres Bordeaux

17 (2005), no. 3, 825--858 (with M. Smorodinsky).

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21. On polynomially normal lattice configurations. Monatsh. Math.

147 (2006), no. 2, 137--153 (with M. Smorodinsky).

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22. Discrepancy estimates of normal vectors, Unif. Distrib.

Theory 3 (2008), no. 1, 19-33. (with I. Volinsky)

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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.

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24. Adelic constructions of low discrepancy sequences, Online J. Anal. Comb.

. No. 5 (2010), 27

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25. Discrepancy estimate of normal vectors (the case of hyperbolic matrices) Unif. Distrib. Theory

5 (2010), no. 2, 141-167. (with I. Volinsky)

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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)

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27. Central Limit Theorem for $Z_{+}^d$-actions by toral endomorphisms, Electronic Journal of Probability,

18 (2013), no. 35, 42~pp.

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28 A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series, Colloq. Mathem.

131 (2013), no. 1, 13-27.

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29. On Gaussian limiting distribution of lattice points in a parallelepiped,\\ http://arxiv.org/abs/1307.2076, 42 p.

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30. On the lower bound in the lattice point remainder problem for a parallelepiped, http://arxiv.org/abs/1307.2080, 48 p.\\

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31. On the lower bound of the discrepancy of Halton's sequence: I,\\

http://arxiv.org/abs/1412.8705,

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32. On the lower bound of the discrepancy of (t,s) sequence: I,\\

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PhD students I. Volinskay (graduated in 2011), N. Sharuf