Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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.

Let (s,t,u in {{mathbb {C}}}) and T(s, t, u) be the Tornheim double zeta function. In this paper, we investigate some properties of symmetric Tornheim double zeta functions which can be regarded as a desingularization of the Tornheim double zeta function. As a corollary, we give explicit evaluation formulas or rapidly convergent series representations for T(s, t, u) in terms of series of the gamma function and the Riemann zeta function.

The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of (E_infty )-ring spectra in various ways. In this work we first establish, in the context of (infty )-categories and using Goodwillie’s calculus of functors, that various definitions of the cotangent complex of a map of (E_infty )-ring spectra that exist in the literature are equivalent. We then turn our attention to a specific example. Let R be an (E_infty )-ring spectrum and (mathrm {Pic}(R)) denote its Picard (E_infty )-group. Let Mf denote the Thom (E_infty )-R-algebra of a map of (E_infty )-groups (f:Grightarrow mathrm {Pic}(R)); examples of Mf are given by various flavors of cobordism spectra. We prove that the cotangent complex of (Rrightarrow Mf) is equivalent to the smash product of Mf and the connective spectrum associated to G.

Let (pod_3(n)) denote the number of 3-regular partitions of n with distinct odd parts (and even parts are unrestricted). In this article, we prove an infinite family of congruences for (pod_3(n)) using the theory of Hecke eigenforms. We also study the divisibility properties of (pod_3(n)) using arithmetic properties of modular forms.