Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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).

Suppose (q=p^r), where p is a prime congruent to 3 or 5 modulo 8 and r is odd or (q = 2^r) for any r. Then every closed smooth ({text {PSL}}(2,q)) manifold has a strongly algebraic model.

By introducing a new approximation technique in the (L^2) theory of the (bar{partial })-operator, Hörmander’s (L^2) variant of Andreotti-Grauert’s finiteness theorem is extended and refined on q-convex manifolds and weakly 1-complete manifolds. As an application, a question on the (L^2) cohomology suggested by a theory of Ueda (Tohoku Math J (2) 31(1):81–90, 1979), Ueda (J Math Kyoto Univ 22(4):583–607, 1982/83) is solved.

In 1900, at the international congress of mathematicians, Hilbert claimed that the Riemann zeta function (zeta (s)) is not the solution of any algebraic ordinary differential equations on its region of analyticity. In 2015, Van Gorder (J Number Theory 147:778–788, 2015) considered the question of whether (zeta (s)) satisfies a non-algebraic differential equation and showed that it formally satisfies an infinite order linear differential equation. Recently, Prado and Klinger-Logan (J Number Theory 217:422–442, 2020) extended Van Gorder’s result to show that the Hurwitz zeta function (zeta (s,a)) is also formally satisfies a similar differential equation

But unfortunately in the same paper they proved that the operator T applied to Hurwitz zeta function (zeta (s,a)) does not converge at any point in the complex plane ({mathbb {C}}). In this paper, by defining (T_{p}^{a}), a p-adic analogue of Van Gorder’s operator T,  we establish an analogue of Prado and Klinger-Logan’s differential equation satisfied by (zeta _{p,E}(s,a)) which is the p-adic analogue of the Hurwitz-type Euler zeta functions

In contrast with the complex case, due to the non-archimedean property, the operator (T_{p}^{a}) applied to the p-adic Hurwitz-type Euler zeta function (zeta _{p,E}(s,a)) is convergent p-adically in the area of (sin {mathbb {Z}}_{p}) with (sne 1) and (ain K) with (|a|_{p}>1,) where K is any finite extension of ({mathbb {Q}}_{p}) with ramification index over ({mathbb {Q}}_{p}) less than (p-1.)

We look at genera of even unimodular lattices of rank 12 over the ring of integers of ({{mathbb {Q}}}(sqrt{5})) and of rank 8 over the ring of integers of ({{mathbb {Q}}}(sqrt{3})), using Kneser neighbours to diagonalise spaces of scalar-valued algebraic modular forms. We conjecture most of the global Arthur parameters, and prove several of them using theta series, in the manner of Ikeda and Yamana. We find instances of congruences for non-parallel weight Hilbert modular forms. Turning to the genus of Hermitian lattices of rank 12 over the Eisenstein integers, even and unimodular over ({{mathbb {Z}}}), we prove a conjecture of Hentschel, Krieg and Nebe, identifying a certain linear combination of theta series as an Hermitian Ikeda lift, and we prove that another is an Hermitian Miyawaki lift.

Inspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kähler manifolds satisfying the (Delta )-property, i.e. such that on a neighborhood of each of its points the k-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kähler manifold satisfies the (Delta )-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.