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 ?(s+i?,F) of zeta-functions of normalized Hecke-eigen forms F, where ? takes values from the set {k?h:k=0,1,2,...} with fixed 0 < ? < 1 and h > 0, is obtained.

On the distribution of a linear sequence associated to sum of divisors evaluated at polynomial arguments

Following the recent method of Deshouillers and the author in the theory of distribution modulo 1, we show that the sequence with general term bn = ?m?n(m2 + 1)/?(m2 + 1) is dense modulo 1.