The residues modulo m of products of random integers

Autor(en): Stadje, W 
Stichwörter: Computer Science; Computer Science, Theory & Methods; Mathematics; Statistics & Probability
Erscheinungsdatum: 2002
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: COMBINATORICS PROBABILITY & COMPUTING
Volumen: 11
Ausgabe: 5
Startseite: 529
Seitenende: 540
Zusammenfassung: 
For two stochastically dependent random variables X and Y taking values in {0,..., m - 1}, we study the distribution of the random residue U = XY mod in. Our main result is an upper bound for the distance Delta(m) = sup(xis an element of[0,1]) P(U/m less than or equal to x) - x. For independent and uniformly distributed X and Y, the exact distribution of U is derived and shown to be stochastically smaller than the uniform distribution on {0,..., m - 1}. Moreover, in this case Delta(m) is given explicitly.
ISSN: 09635483
DOI: 10.1017/S0963548302005308

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