On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period

Monatshefte fur Mathematik

Volumn 129, Issue 1, 2000, Pages 31-36

  Gutierrez, Jaime ^a   Niederreiter, Harald ^b   Shparlinski, Igor E ^c  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c University of Cantabria ^*

Author keywords

Discrepancy; Exponential sums; Inversive congruential method; Pseudorandom numbers

Indexed keywords

EID: 0002966966     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050050004     Document Type: Article

References (17)

1. EICHENAUER-HERRMANN J, EMMERICH F (1996) Compound inversive congruential pseudorandom numbers: an average-case analysis. Math Comp 65: 215-225
2. EICHENAUER-HERRMANN J, EMMERICH F, LARCHER G (1997) Average discrepancy, hyperplanes, and compound pseudorandom numbers. Finite Fields Appl 3: 203-218
3. EICHENAUER-HERRMANN J, HERRMANN E, WEGENKITTL S (1998) A survey of quadratic and inversive congruential pseudorandom numbers. Lect Notes Statistics 127: 66-97 Berlin Heidelberg New York: Springer
4. FLAHIVE M, NIEDERREITER H (1993) On inversive congruential generators for pseudorandom numbers. In: MULLEN GL, SHIUE PJ-S (eds) Finite Fields, Coding Theory, and Advances in Communications and Computing, pp 75-80. New York: Dekker
5. FRIEDLANDER JB, LIEMAN D, SHPARLINSKI IE (1999) On the distribution of the RSA generator. In: DING C, HELLESETH T, NIEDERREITER H (eds) Sequences and Their Applications, pp 205-212. London: Springer
6. ISMOILOV D (1994) Estimates for complete trigonometric sums. Trudy Mat Inst Steklov 207: 153-171 (in Russian)
7. ISMOILOV D (1994) On a method of Hua Loo-Keng of estimating complete trigonometric sums. Adv in Math (China) 23: 31-49
8. LIDL R, NIEDERREITER H (1996) Finite fields and their applications. In: HAZEWINKEL M (ed) Handbook of Algebra, Vol. 1, 321-363 Amsterdam: Elsevier
9. LIDL R, NIEDERREITER H (1997) Finite Fields. Cambridge: Univ Press
10. MORENO CJ, MORENO O (1991) Exponential sums and Goppa codes, I. Proc Amer Math Soc 111: 523-531
11. NIEDERREITER H (1989) The serial test for congruential pseudorandom numbers generated by inversions. Math Comp 52: 135-144
12. NIEDERREITER H (1992) Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: SIAM
13. NIEDERREITER H (1993) Finite fields, pseudorandom numbers, and quasirandom points. In: MULLEN GL, SHIUE PJ-S (eds) Finite Fields, Coding Theory, and Advances in Communications and Computing, pp 375-394. New York: Dekker
14. NIEDERREITER H (1995) New developments in uniform pseudorandom number and vector generation. Lect Notes Statistics 106: 87-120. Berlin Heidelberg New York: Springer
15. NIEDERREITER H, SHPARLINSKI IE (1998) On the distribution of inversive congruential pseudorandom numbers in parts of the period (preprint)
16. NIEDERREITER H, SHPARLINSKI IE (1999) On the distribution and lattice structure of nonlinear congruential pseudorandom numbers. Finite Fields Appl 5: 246-253
17. STECKIN SB (1977) An estimate of a complete rational exponential sum. Trudy Mat Inst Steklov 143: 188-207 (in Russian)