Here we solve Durfee's conjecture for 2-dimensional hypersurface singularities of multiplicity 3. We show that the Milnor number is greater than or equal to six times the geometric genus plus two in this case. The equality holds if and only if it is a simple elliptic singularity. For the proof, we consider an analog for triple coverings of Horikawa's canonical resolution for double coverings. We express these invariants in terms of our resolution process and the covering base surface.
We give conditions on pairs of weight functions for which a certainoperator defined on Ω ⊆ R2+ is bounded between weighted Lorentz spaces. The result isapplied to obtain weighted estimates for the Laplace transform.
A certain formal power series attached to local densities of quadratic forms is defined. It is shown that this series can be realized as a coefficient of the Laurent expansion of a generalized Igusa local zeta function.
Let Q be the rational number field, l an odd prime number, n a positive integer, and m_i(1 ≤ i ≤ n) rational numbers. In this paper we find an integral basis for a field K={Q}(m1/l_1, m1/l_2, ..., m1/l_n) and determine the discriminant of K. When n=2 and m_1=1, an integral basis for K was found by Komatsu [1].
A free boundary problem for a nonlinear second order differential equation involving a small parameter is studied. The problem arises in the research of certain generalized diffusion processes. Its solution is constructed by the aid of the unique solution of a two-point boundary value problem for two nonlinear first order differential equations, in which the right endpoint is singular.
Smooth SL(n, {C})-actions on (2_n-1)-manifolds were classified by Uchida [12], while smooth SL(2, {H})-actions on 7-manifolds are discussed in Abe [1]. In this paper, the classification of smooth actions of SL(n, {H}) and Sp(n, {C}) on simply connected closed (4_n-1)-manifolds is carried out for n ≥q 3.
We derive higher order variational formulas for the Yamabe functional, and give an example of infinitesimal deformation of a solution of the Yamabe problem which does not come from conformal vector field.
In 1982, Fuchs raised the following conjecture: Suppose that F is an entire function of finite order with at least one finite deficient value. Then F is pseudo-prime. In this paper, we prove this conjecture under the additional condition that the number of the limiting directions of Julia directions of F is finite.
We are concerned with complex dynamics of iteration of an entiretranscendenta1 function as in the title of this paper and discuss the following Problem: For what value of the real parameter μ does the Julia set of the function coincide withthe whole complex plane?
This paper is concerned with Cesàro summability and Marcinkiewicz multipliers for the n-dimensional case of Laguerre expansions of a different kind. The results are obtained from the corresponding results for the n-dimensional Hennite expansions by appealing to a transplantation theorem which is also proved here.