On the iwasawa algebra associated to a normal element of ℂ<Subscript><Emphasis Type=Italic>p</Emphasis></Subscript>

Given a prime number p and the Galois orbit O(x) of a normal element x of ℂ _p , the topological completion of the algebraic closure of the field of p-adic numbers, we study the Iwasawa algebra of O(x) with scalars drawn from ℚ _p and relate it with ℚ _p -distributions and functionals.     

Invariance of cohomologicalq-completeness under finite holomorphic surjections

It is proved that cohomologicalq-completeness (cohomologicalq-convexity) is invariant under finite surjective holomorphic mappings. A related result in the non-proper case is also proved.     

An application of q-concavity to increasing sequences of Stein open sets

We prove that in a normal Stein space a relatively compact open set is a domain of holomorphy provided that it is an increasing union of Stein open subspaces. Received: 13 December 2004     

On the Existence of Trace for Elements of \mathbb{C}_p

Let T be a transcendental element of and the orbit of T. On we have a Haar measure . The goal of this paper is to characterize all the elements of for which the integral , called the trace of T, is well defined.Presented by A. Verschoren     

On the index of fractions with square-free denominators in arithmetic progressions

We prove asymptotic formulas for the first and second moments of the index of fractions with square-free denominators of order Q streaming in a given arithmetic progression as Q→∞. A. Zaharescu was supported by NSF grant number DMS-0456615. This research was also partially supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.     

Distinct gaps between fractional parts of sequences

Let be a real number, a positive integer and a subset of . We give an upper bound for the number of distinct lengths of gaps between the fractional parts .