Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

Assume a and (b=na+r) with (n ge 1) and (0<r<a) are relatively prime integers. In case C is a smooth curve and P is a point on C with Weierstrass semigroup equal to (<a;b>) then C is called a (C_{a;b})-curve. In case (r ne a-1) and (b ne a+1) we prove C has no other point (Q ne P) having Weierstrass semigroup equal to (<a;b>), in which case we say that the Weierstrass semigroup (<a;b>) occurs at most once. The curve (C_{a;b}) has genus ((a-1)(b-1)/2) and the result is generalized to genus (g<(a-1)(b-1)/2). We obtain a lower bound on g (sharp in many cases) such that all Weierstrass semigroups of genus g containing (<a;b>) occur at most once.

We prove the existence of meromorphic continuation and the functional equation of the real analytic Jacobi Eisenstein series of degree m and matrix index T in case T is a kernel form.

In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The paper focuses on the Hilbert modular forms over real quadratic fields. We will state a construction of relations between the special values of L-functions, especially at 0, and arithmetic functions. We will also give a relation between the sum of squares functions with underlying fields (mathbb {Q}(sqrt{D})) and (mathbb {Q}).

Generalized Burniat surfaces are surfaces of general type with (p_g=q) and Euler number (e=6) obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.

In the 1960s Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct (chi _{5}), the cusp form of lowest weight for the group ({text {Sp}}(2,mathbb {Z})). In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identified with the orthogonal group of signature (2, 3) for the lattice (A_{1}) and Igusa’s form (chi _{5}) appears as the roof of this tower. We use this interpretation to construct a framework for this tower which uses three different types of constructions for modular forms. It turns out that our method produces simple coordinates.

In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field K of a curve over an algebraically closed field: there is a perfect duality of finite groups for F a finite étale Galois module on K of order invertible in K and with (F' = {{mathrm{Hom}}}(F,mathbf{Q}/mathbf {Z}(1))). Furthermore, we prove that (mathrm {H}^1(K,G) = 0) for G a simply connected, quasisplit semisimple group over K not of type (E_8).

We develop the classification of weakly symmetric pseudo-Riemannian manifolds G / H where G is a semisimple Lie group and H is a reductive subgroup. We derive the classification from the cases where G is compact, and then we discuss the (isotropy) representation of H on the tangent space of G / H and the signature of the invariant pseudo-Riemannian metric. As a consequence we obtain the classification of semisimple weakly symmetric manifolds of Lorentz signature ((n-1,1)) and trans-Lorentzian signature ((n-2,2)).

We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.

This paper is devoted, first of all, to give a complete unified proof of the characterization theorem for compact generalized Kähler manifolds. The proof is based on the classical duality between “closed” positive forms and “exact” positive currents. In the last part of the paper we approach the general case of non compact complex manifolds, where “exact” positive forms seem to play a more significant role than “closed” forms. In this setting, we state the appropriate characterization theorems and give some interesting applications.