TY - JOUR

T1 - Distribution of a sparse set of fractions modulo q

AU - Cobeli, Cristian

AU - Zaharescu, Alexandru

PY - 2001/3

Y1 - 2001/3

N2 - The distribution on the torus ℝ/ℤ of a set of fractions of the form script R = {um̄R(n) (mod q)/q : u ∈ script U, m ∈ script M, n ∈ script N} is investigated, where q is a large integer, m̄ is the inverse of m modulo q, R(x) is a rational function defined modulo q, and script U, script M, script N are subsets of {1, ..., q}. Under some natural assumptions, it is shown that the set script R is uniformly distributed on ℝ/ℤ.

AB - The distribution on the torus ℝ/ℤ of a set of fractions of the form script R = {um̄R(n) (mod q)/q : u ∈ script U, m ∈ script M, n ∈ script N} is investigated, where q is a large integer, m̄ is the inverse of m modulo q, R(x) is a rational function defined modulo q, and script U, script M, script N are subsets of {1, ..., q}. Under some natural assumptions, it is shown that the set script R is uniformly distributed on ℝ/ℤ.

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U2 - 10.1112/blms/33.2.138

DO - 10.1112/blms/33.2.138

M3 - Article

AN - SCOPUS:0039895952

VL - 33

SP - 138

EP - 148

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 2

ER -