Locally GCD domains and the ring $D+XD_S[X]$

Harmonic Measure and “ Locally Flat ” Domains ∗

We will review work with Tatiana Toro yielding a characterization of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation. 2000 Mathematics Subject Classification: 31B25, 35R35, 42B35, 51M25.

Efficient Algorithms for GCD and Cubic Residuosity in the Ring of Eisenstein Integers

We present simple and efficient algorithms for computing gcd and cubic residuosity in the ring of Eisenstein integers, Z[ζ], i.e. the integers extended with ζ, a complex primitive third root of unity. The algorithms are similar and may be seen as generalisations of the binary integer gcd and derived Jacobi symbol algorithms. Our algorithms take time O(n2) for n bit input. This is an improvement...

Locally Uniform Domains and Quasiconformal Mappings

We document various properties of the classes of locally uniform and weakly linearly locally connected domains. We describe the boundary behavior for quasiconformal ho-meomorphisms of these domains and exhibit certain metric conditions satissed by such maps. We characterize the quasiconformal homeomorphisms from locally uniform domains onto uniform domains. We furnish conditions which ensure th...

The gcd-sum function

The gcd-sum is an arithmetic function defined as the sum of the gcd’s of the first n integers with n : g(n) = ∑n i=1(i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of par...

Sobolev Cohomology for Locally Polycylindrical Domains

The Locally F-approximation Property of Bounded Hyperconvex Domains

In this paper, we study the local property of bounded hyperconvex domains Ω which we can approximative each plurisubharmonic function u ∈ F(Ω) by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.