Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus
Harald Niederreiter ; Igor E. Shparlinski
Acta Arithmetica, Tome 92 (2000), p. 89-98 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207371
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     author = {Harald Niederreiter and Igor E. Shparlinski},
     title = {Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus},
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {89-98},
     zbl = {0949.11036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav92i1p89bwm}
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Harald Niederreiter; Igor E. Shparlinski. Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus. Acta Arithmetica, Tome 92 (2000) pp. 89-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav92i1p89bwm/

[000] [1] W.-S. Chou, The period lengths of inversive congruential recursions, Acta Arith. 73 (1995), 325-341. | Zbl 0852.11038

[001] [2] J. Eichenauer-Herrmann, E. Herrmann and S. Wegenkittl, A survey of quadratic and inversive congruential pseudorandom numbers, in: Monte Carlo and Quasi-Monte Carlo Methods 1996, H. Niederreiter et al. (eds.), Lecture Notes in Statist. 127, Springer, New York, 1998, 66-97. | Zbl 0885.65003

[002] [3] J. Eichenauer-Herrmann and H. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), 243-249. | Zbl 0731.11046

[003] [4] J. Eichenauer-Herrmann and A. Topuzoğlu, On the period length of congruential pseudorandom number sequences generated by inversions, ibid. 31 (1990), 87-96. | Zbl 0704.65001

[004] [5] F. Griffin, H. Niederreiter and I. E. Shparlinski, On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders, in: Proc. 13th Sympos. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, 1999, Lecture Notes in Comput. Sci., Springer, Berlin, to appear. | Zbl 0958.11052

[005] [6] J. Gutierrez, H. Niederreiter and I. E. Shparlinski, On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period, Monatsh. Math., to appear. | Zbl 1011.11053

[006] [7] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983; reprint, Cambridge Univ. Press, Cambridge, 1997. | Zbl 0554.12010

[007] [8] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.

[008] [9] H. Niederreiter, New developments in uniform pseudorandom number and vector generation, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P.J.-S. Shiue (eds.), Lecture Notes in Statist. 106, Springer, New York, 1995, 87-120. | Zbl 0893.11030

[009] [10] H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, preprint, 1998. | Zbl 0983.11048

[010] [11] H. Niederreiter and I. E. Shparlinski, On the distribution and lattice structure of nonlinear congruential pseudorandom numbers, Finite Fields Appl. 5 (1999), 246-253. | Zbl 0942.11037

[011] [12] H. Niederreiter and I. E. Shparlinski, On the distribution of pseudorandom numbers and vectors generated by inversive methods, Appl. Algebra Engrg. Comm. Comput., to appear. | Zbl 0999.11040

[012] [13] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1932), 91-109.

[013] [14] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 183-216. | Zbl 0575.42003