On $n$-dimensional uniform distribution modulo $1$.

On uniform distribution modulo one

We introduce an elementary argument to the theory of distribution of sequences modulo one.

On the Distribution of Inverses Modulo n

Uniform Distribution modulo 1 of the Harmonic Prime Factor of an Integer

for the arithmetic mean of the distinct prime factors of n, then pa(n) is uniformly distributed modulo 1. Furthermore, it was also shown that for large x the number of n ≤ x such that pa(n) is an integer of order of magnitude O(x/ log log x). This was made more precise by the first author in [4], who showed that the counting function of the above n is asymptotically equal to (c+o(1))x/ log log ...

Uniform Distribution modulo 1 and the Universality of Zeta-functions of Certain Cusp Forms

An universality theorem on the approximation of analytic functions by shifts ζ(s+iτ, F ) of zeta-functions of normalized Hecke-eigen forms F , where τ takes values from the set {kαh : k = 0, 1, 2, . . . } with fixed 0 < α < 1 and h > 0, is obtained.

Distribution of Powers modulo 1 and Relatedtopicsmiguel

This is a review of several results related to distribution of powers and combinations of powers modulo 1. We include a proof that given any sequence of real numbers n , it is possible to get an (given 6 = 0), or a (given > 1) such that n is close to n modulo 1. We also prove that in a number eld, if a combination of powers 1 n 1 + + m n m has bounded v-adic absolute value (where v is any non-A...