We give explicit upper bounds for the discriminants of the non-normal quartic CM-fields with class number one, and for the discriminants of the dihedral octic CM-fields with class number one. These upper bounds are too large to enable us to achieve the determination of these number fields. Nevertheless, whenever a real quadratic number field k is fixed, we can explain how to determine the non-normal quartic CM-fields or the dihedral octic CM-fields with class number one and with real quadratic subfield k.
Direct theorems of Jackson type on estimating the degree of the best approximation in Banach spaces are obtained by means of the moduli of continuity of higher orders of elements having certain smoothness properties.
M. Eichler and D. Zagier constructed a map from a space of Jacobi forms to a space of elliptic modular forms. On the other hand, T. Satoh constructed a map from a space of cusp forms to a space of Jacobi cusp forms. In this paper, we prove a conjecture of N. P. Skoruppa to the effect that these maps are, up to constant, adjoint with respect to the Petersson products.
Generic conditions for the occurrence of a parabolic subgroup of given type in a reductive algebraic group are described. Especially the notion of a generic splitting field of a reductive algebraic group is investigated. The given theory generalizes and unifies other investigations of various authors for special algebraic structures such as Azumaya algebras and quadratic forms.
We are concerned with the qualitative theory of high codimension foliations. In order to restrict the object of our study, we consider the actions of a pseudogroup of local similarity transformations of a Euclidean space. For an orbit "with bubbles" of such an action, we obtain analogs of the qualitative properties of codimension one foliations.
We investigate the heat-diffusion and Poisson integrals for expansions with respect to three different systems of Laguerre functions. The main achievements of the paper are the weak type (1, 1) estimates for the associated maximal functions.
We prove a property of left cells in certain crystallographic groups W, by which we formulate an algorithm to find a representative set of left cells of W in any given two-sided cell. As an illustration, we make some applications of this algorithm to the case where W is the affine Weyl group of type F4.
Earlier the author gave the classification of Einstein-Kähler toric Fano fourfolds except in one case. In the present paper, we prove the existence of Einstein-Kahler metrics on some family of Fano manifolds including the remaining toric Fano fourfold. In particular, we completely classify the Einstein-Kähler toric Fano fourfolds.
The universal Teichmüller space contains all Teichmüller spaces of hyperbolic Riemann surfaces. We shall investigate how the Teichmüller spaces of punctured spheres vary in the universal Teichmüller space when the base points change.