Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

We show that a dihedral congruence prime for a normalised Hecke eigenform f in (S_k(Gamma _0(D),chi _D)), where (chi _D) is a real quadratic character, appears in the denominator of the Bloch–Kato conjectural formula for the value at 1 of the twisted adjoint L-function of f. We then use a formula of Zagier to prove that it appears in the denominator of a suitably normalised (L(1,{mathrm {ad}}^0(g)otimes chi _D)) for some (gin S_k(Gamma _0(D),chi _D)).

We show that a hypersurface of the regularized, spatial circular restricted three-body problem is of contact type whenever the energy level is below the first critical value (the energy level of the first Lagrange point) or if the energy level is slightly above it. A dynamical consequence is that there is no blue sky catastrophe in this energy range.

We study finite dimensional almost- and quasi-effective prolongations of nilpotent ({mathbb {Z}})-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi–Malčev and Levi–Chevalley decompositions and precisions on the heigth and other properties of the prolongations in a very natural way. In a last section we consider the semisimple case and discuss some examples in which the structural algebras are central extensions of orthogonal Lie algebras and their degree ((-,1)) components arise from spin representations.

We derive the existence of p-adic Hurwitz–Lerch L-function by means of a method provided by Washington. This function is a generalization of the one-variable p-adic L-function of Kubota and Leopoldt, and two-variable p-adic L-function of Fox. We also deduce divisibility properties of generalized Apostol–Bernoulli polynomials, in particular establish Kummer-type congruences for them.

Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kähler manifolds satisfying the (Delta)-property, i.e. such that on a neighborhood of each of its points the kth power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove two results: (1) if a Kähler manifold satisfies the (Delta)-property then its curvature tensor is parallel; (2) if an Hermitian symmetric space of classical type satisfies the (Delta)-property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a Kähler manifold satisfies the (Delta)-property then it is a complex space form.

In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principal, Gaussian, and mean curvatures in terms of the eigenvalues of the differential of this map. Considering planar sections containing the normal field, we also define normal curvatures at each point of the surface, and with respect to each tangent direction. We investigate the relations between these curvature types. Further on we prove that, under an additional hypothesis, a compact, connected surface without boundary whose Minkowski Gaussian curvature is constant must be a Minkowski sphere. Since existing literature on the subject of our paper is widely scattered, in the introductory part also a survey of related results is given.

We show that certain Fano eightfolds (obtained as hyperplane sections of an orthogonal Grassmannian, and studied by Ito–Miura–Okawa–Ueda and by Fatighenti–Mongardi) have a multiplicative Chow–Künneth decomposition. As a corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.

In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit into this context (as for example banachanalytic spaces, Kähler spaces etc.)

Let p be an odd prime number. We construct explicit uniformizers for the totally ramified extension ({mathbb {Q}}_p(zeta _{p^2},root p of {p})) of the field of p-adic numbers ({mathbb {Q}}_p), where (zeta _{p^2}) is a primitive (p^2)-th root of unity.

For an arbitrary real connected Lie group G we define (mathrm {p}(G)) as the maximal integer p such that (mathbb {Z}^p) is isomorphic to a discrete subgroup of G and (mathrm {q}(G)) is the maximal integer q such that (mathbb {R}^q) is isomorphic to a closed subgroup of G. The aim of this paper is to investigate properties of these two invariants. We will show that if G is a noncompact connected Lie group, then (1le mathrm {q}(G)le mathrm {p}(G)le dim (G/K)) where K is a maximal compact subgroup of G. In the cases when G is an exponential Lie group or G is a connected nilpotent Lie group, we give explicit relationships between these two invariants and a well known Lie algebra invariant (mathcal M(mathfrak {g})), i.e. the maximum among the dimensions of abelian subalgebras of the Lie algebra (mathfrak {g}:=mathrm {Lie}(G)).