ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

Note on regular and coregular sequences

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

On Runs in Independent Sequences

Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.

Kronecker-type sequences and nonarchimedean diophantine approximations

xn = ({nα1}, . . . , {nαs}) , n = 0, 1, . . . , where {u} is the fractional part of u ∈ R. It is well known that the sequence x0,x1, . . . is uniformly distributed in I = [0, 1] if and only if 1, α1, . . . , αs are linearly independent over Q, and that the finer quantitative description of the distribution behavior of this sequence depends on the diophantine approximation character of the point...

On Reducing sequences and an Application to Local Cohomology Modules

Equidistribution of Kronecker Sequences along Closed Horocycles

It is well known that (i) for every irrational number α the Kronecker sequence mα (m = 1, . . . ,M) is equidistributed modulo one in the limit M → ∞, and (ii) closed horocycles of length l become equidistributed in the unit tangent bundle T1M of a hyperbolic surface M of finite area, as l → ∞. In the present paper both equidistribution problems are studied simultaneously: we prove that for any ...