The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.

# Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

### Description

### Identifiers

ISSN | 0025-5858 |

e-ISSN | 1865-8784 |

DOI | 10.1007/12188.1865-8784 |

### Publisher

Springer Berlin Heidelberg

### Additional information

Data set: Springer

### Articles

We prove that at least one of the six numbers $$\beta (2i)$$ β ( 2 i ) for $$i=1,\ldots ,6$$ i = 1 , … , 6 is irrational. Here $$\beta (s)=\sum _{k=0}^{\infty }(-1)^k(2k+1)^{-s}$$ β ( s ) = ∑ k = 0 ∞ ( - 1 ) k ( 2 k + 1 ) - s denotes Dirichlet’s beta function, so that $$\beta (2)$$ β ( 2 ) is Catalan’s constant.

Assume

*a*and $$b=na+r$$ b = n a + r with $$n \ge 1$$ n ≥ 1 and $$0<r<a$$ 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 $$<a;b>$$ < a ; b > then*C*is called a $$C_{a;b}$$ C a ; b -curve. In case $$r \ne a-1$$ r ≠ a - 1 and $$b \ne a+1$$ b ≠ a...
The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in $${\mathbb {R}}^{n+2}$$ R n + 2 , isotropic surfaces in $$S^4$$ S 4 and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in $$S^6$$ S 6 without dual surfaces is also presented.