Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

We state and prove a formula for the adjoint of the nullwert map from spaces of Jacobi cusp forms of lattice index to spaces of modular forms. Furthermore, we prove a nonvanishing result for the image of the adjoint of the nullwert map.

In this paper we study the theta lifting of a weight 2 Bianchi modular form ({mathcal {F}}) of level (Gamma _0({mathfrak {n}})) with ({mathfrak {n}}) square-free to a weight 2 holomorphic Siegel modular form. Motivated by Prasanna’s work for the Shintani lifting, we define the local Schwartz function at finite places using a quadratic Hecke character (chi ) of square-free conductor ({mathfrak {f}}) coprime to level ({mathfrak {n}}). Then, at certain 2 by 2 g matrices (beta ) related to ({mathfrak {f}}), we can express the Fourier coefficient of this theta lifting as a multiple of (L({mathcal {F}},chi ,1)) by a non-zero constant. If the twisted L-value is known to be non-vanishing, we can deduce the non-vanishing of our theta lifting.

To any V in the Grassmannian (textrm{Gr}_k({mathbb R}^n)) of k-dimensional vector subspaces in ({mathbb {R}}^n) one can associate the diagonal entries of the ((ntimes n)) matrix corresponding to the orthogonal projection of ({mathbb {R}}^n) to V. One obtains a map (textrm{Gr}_k({mathbb {R}}^n)rightarrow {mathbb {R}}^n) (the Schur–Horn map). The main result of this paper is a criterion for pre-images of vectors in ({mathbb {R}}^n) to be connected. This will allow us to deduce connectivity criteria for a certain class of subspaces of the real Stiefel manifold which arise naturally in frame theory. We extend in this way results of Cahill et al. (SIAM J Appl Algebra Geom 1:38–72, 2017).

Let X be a K3 surface, let C be a smooth curve of genus g on X, and let A be a line bundle of degree d on C. Then a line bundle M on X with (Motimes {mathcal {O}}_C=A) is called a lift of A. In this paper, we prove that if the dimension of the linear system |A| is (rge 2), (g>2d-3+(r-1)^2), (dge 2r+4), and A computes the Clifford index of C, then there exists a base point free lift M of A such that the general member of |M| is a smooth curve of genus r. In particular, if |A| is a base point free net which defines a double covering (pi :Clongrightarrow C_0) of a smooth curve (C_0subset {mathbb {P}}^2) of degree (kge 4) branched at distinct 6k points on (C_0), then, by using the aforementioned result, we can also show that there exists a 2:1 morphism ({tilde{pi }}:Xlongrightarrow {mathbb {P}}^2) such that ({tilde{pi }}|_C=pi ).

Let K be a number field and G a finitely generated torsion-free subgroup of (K^times ). Given a prime (mathfrak {p}) of K we denote by ({{,textrm{ind},}}_mathfrak {p}(G)) the index of the subgroup ((Gbmod mathfrak {p})) of the multiplicative group of the residue field at (mathfrak {p}). Under the Generalized Riemann Hypothesis we determine the natural density of primes of K for which this index is in a prescribed set S and has prescribed Frobenius in a finite Galois extension F of K. We study in detail the natural density in case S is an arithmetic progression, in particular its positivity.

In this paper, when (1<p<2), we establish the (C^{1,alpha }_{,textrm{loc},})-regularity of weak solutions to the degenerate subelliptic p-Laplacian equation

on SU(3) endowed with the horizontal vector fields (X_1,dots ,X_6). The result can be extended to a class of compact connected semi-simple Lie group.

In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form ({mathbb {L}}^4(delta )) with constant sectional curvature (delta ). We obtain some local classifications of biconservative CMC surfaces in ({mathbb {L}}^4(delta )). Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space.

We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For (nin {2,3,4}), we show that, generically in all but a finite number of irreducible components of the moduli space of polarized (textrm{Kum}^n)-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.

In his 2008 thesis [16] , Tateno claimed a counterexample to the Bonato–Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno’s unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides partial orders with a similar conclusion. At the same time these examples also disprove conjectures by Thomassé and Tyomkyn.