Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

In this paper, we consider a kind of area-preserving flow for closed convex planar curves which will decrease the length of the evolving curve and make the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle as time (trightarrow +infty ).

Let X be a smooth quintic hypersurface in (mathbb {P}^3), let C be a smooth hyperplane section of X, and let (H=mathcal {O}_X(C)). In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero effective divisor on X to be initialized and aCM with respect to H.

We study p-adic L-functions (L_p(s,chi )) for Dirichlet characters (chi ). We show that (L_p(s,chi )) has a Dirichlet series expansion for each regularization parameter c that is prime to p and the conductor of (chi ). The expansion is proved by transforming a known formula for p-adic L-functions and by controlling the limiting behavior. A finite number of Euler factors can be factored off in a natural manner from the p-adic Dirichlet series. We also provide an alternative proof of the expansion using p-adic measures and give an explicit formula for the values of the regularized Bernoulli distribution. The result is particularly simple for (c=2), where we obtain a Dirichlet series expansion that is similar to the complex case.

The moduli spaces of flat ({text{SL}}_2)- and ({text{PGL}}_2)-connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.

We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in ({mathbb {Q}}(sqrt{-7})) and ({mathbb {Q}}(sqrt{-11})). In both cases we prove that the subrings of symmetric modular forms are generated by Maass lifts. The computation uses a reduction process against Borcherds products which also leads to a dimension formula for the spaces of modular forms.

We identify the p-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic p as the eigenvalues of a product of special values of a certain matrix of p-adic series. That matrix is a product (F(varLambda ^p)^{-1}F(varLambda )), where the entries in the matrix (F(varLambda )) are A-hypergeometric series with integral coefficients and (F(varLambda )) is independent of p.

Motivated by calculations of motivic homotopy groups, we give widely attained conditions under which operadic algebras and modules thereof are preserved under (co)localization functors.

In this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and (0<h(n) le h(n+1)). We put (P_0^{g,h}(x)=1) and

As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind (eta )-function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where (G = G_1 ldots G_l) is a connected semisimple Lie group without compact factors whose Lie algebra is ({mathfrak {g}}= {mathfrak {g}}_1 oplus {mathfrak {g}}_2 oplus cdots oplus {mathfrak {g}}_l). If (m_0,n_0,n_0^i) are the dimensions of the maximal lightlike subspaces tangent to M, G, (G_i), respectively, then we study G-actions that satisfy the condition (m_0=n_0^1 + cdots + n_0^{l}). This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each (G_i).