Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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).

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.)