第一期“ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG”于 1921 年出版。这本国际数学期刊从那时起为重要的研究贡献提供了一个论坛。该杂志涵盖了纯数学的所有核心领域，例如代数、复分析和几何、微分几何和全局分析、图论和离散数学、李理论、数论和代数拓扑。

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

《Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg》第一期于1921年出版。这本国际数学期刊自创刊以来，为重要的研究成果提供了一个交流平台。期刊涵盖了纯数学的各个核心领域，包括代数、复分析、几何、微分几何、全局分析、图论、离散数学、李理论、数论和代数拓扑等。

Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

Abstract The classical Dedekind sums s ( d , c ) can be represented as sums over the partial quotients of the continued fraction expansion of the rational $$\frac{d}{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:mfrac> </mml:math> . Hardy sums, the analog integer-valued sums arising in the transformation of the logarithms of $$\theta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> -functions under a subgroup of the modular group, have been shown to satisfy many properties which mirror the properties of the classical Dedekind sums. The representation as sums of partial quotients has, however, been missing so far. We define non-classical continued fractions and prove that Hardy sums can be expressed as a sums of partial quotients of these continued fractions. As an application, we prove that the graph of the Hardy sums is dense in $$\textbf{R}\times \textbf{Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>×</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> .

Alessandro Lägeler

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

Continued fractions and Hardy sums

连分数与哈代和

Su Hu

Min-Soo Kim

Infinite order linear difference equation satisfied by a refinement of Goss zeta function

Goss zeta函数细化所满足的无穷阶线性差分方程

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.

Neil Dummigan

Dan Fretwell

Automorphic forms for some even unimodular lattices

一些偶幺模格的自守形式

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 $$\begin{aligned} T\left[ \zeta (s,a) - \frac{1}{a^s}\right] = \frac{1}{(s-1)a^{s-1}}. \end{aligned}$$ 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 $$\begin{aligned} \zeta _E(s,a)=\sum _{n=0}^\infty \frac{(-1)^n}{(n+a)^s}. \end{aligned}$$ 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 $$s\in {\mathbb {Z}}_{p}$$ with $$s\ne 1$$ and $$a\in K$$ with $$|a|_{p}>1,$$ where K is any finite extension of $${\mathbb {Q}}_{p}$$ with ramification index over $${\mathbb {Q}}_{p}$$ less than $$p-1.$$

Infinite order linear differential equation satisfied by p-adic Hurwitz-type Euler zeta functions

无穷阶线性微分方程满足的p进制Hurwitz型欧拉zeta函数

A correction to this paper has been published: https://doi.org/10.1007/s12188-021-00239-x

Takeo Ohsawa

Correction to: Variants of Hörmander’s theorem on q-convex manifolds by a technique of infinitely many weights

更正：通过无穷多权重的技术对q-凸流形上的Hörmander定理的变体

Abstract We extend previous work by constructing a universal abelian tensor category $$\textbf{T}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> generated by two objects X , Y equipped with finite filtrations $$0\subsetneq X_0\subsetneq ...\subsetneq X_{t+1}= X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>⊊</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>⊊</mml:mo> <mml:mo>.</mml:mo> <mml:mo>.</mml:mo> <mml:mo>.</mml:mo> <mml:mo>⊊</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> and $$0\subsetneq Y_0\subsetneq ... \subsetneq Y_{t+1}= Y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>⊊</mml:mo> <mml:msub> <mml:mi>Y</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>⊊</mml:mo> <mml:mo>.</mml:mo> <mml:mo>.</mml:mo> <mml:mo>.</mml:mo> <mml:mo>⊊</mml:mo> <mml:msub> <mml:mi>Y</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>Y</mml:mi> </mml:mrow> </mml:math> , and with a pairing $$X\otimes Y\rightarrow \mathbbm {1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>⊗</mml:mo> <mml:mi>Y</mml:mi> <mml:mo>→</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , where $$\mathbbm {1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> </mml:math> is the monoidal unit. This category is modeled as a category of representations of a Mackey Lie algebra $$\mathfrak {gl}^M(V,V_*)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>gl</mml:mi> </mml:mrow> <mml:mi>M</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mmultiscripts> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of cardinality $$2^{\aleph _t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:msup> </mml:math> , associated to a diagonalizable pairing between two vector spaces $$V,V_*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mmultiscripts> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> </mml:mrow> </mml:math> of dimension $$\aleph _t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> over an algebraically closed field $${{\mathbb {K}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> of characteristic 0. As a preliminary step, we study a tensor category $${{\mathbb {T}}}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> generated by the algebraic duals $$V^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>V</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> and $$(V_*)^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow> <mml:mo>(</mml:mo> <mml:mmultiscripts> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mmultiscripts> </mml:math> . The injective hull of the trivial module $${{\mathbb {K}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> in $${{\mathbb {T}}}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> is a commutative algebra I , and the category $$\textbf{T}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> consists of all free I -modules in $${{\mathbb {T}}}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> . An essential novelty in our work is the explicit computation of Ext-spaces between simples in both categories $$\textbf{T}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> and $${{\mathbb {T}}}_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> , which had been an open problem already for $$t=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . This provides a direct link from the theory of universal tensor categories to Littlewood-Richardson-type combinatorics.

Ivan Penkov

Valdemar Tsanov

Representations of large Mackey Lie algebras and universal tensor categories

大Mackey李代数的表示与通用张量范畴

Abstract A celebrated theorem of Delange gives a sufficient condition for an arithmetic function to be the sum of the associated Ramanujan expansion with the coefficients provided by a previous result of Wintner. By applying the Delange theorem to the correlation of the von Mangoldt function with its incomplete form, we deduce an inequality involving the counting function of the prime numbers in arithmetic progressions. A remarkable aspect is that such an inequality is equivalent to the famous conjectural formula by Hardy and Littlewood for the twin primes.

短名	Abh.Math.Semin.Univ.Hambg.
Journal Impact	0.43
国际分区	MATHEMATICS(Q4)
期刊索引	SCI Q4中科院 4 区

ISSN	0025-5858, 1865-8784
h-index	20
国内分区	数学(4区)数学数学(4区)

涉及主题	数学纯数学几何学数学分析组合数学离散数学微分几何数论域代数上的工程类电气工程拓扑（电路）物理
出版信息	出版商: Springer Verlag，出版周期: Annual，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 2008，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 36.84%
平均审稿周期	网友分享经验：>12周，或约稿
平均录用比例	网友分享经验：容易

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Continued fractions and Hardy sums

Infinite order linear difference equation satisfied by a refinement of Goss zeta function

Automorphic forms for some even unimodular lattices

Infinite order linear differential equation satisfied by p-adic Hurwitz-type Euler zeta functions

Correction to: Variants of Hörmander’s theorem on q-convex manifolds by a technique of infinitely many weights

Continued fractions and Hardy sums

Infinite order linear difference equation satisfied by a refinement of Goss zeta function

Representations of large Mackey Lie algebras and universal tensor categories

On Ramanujan expansions and primes in arithmetic progressions

A Fourier analysis of quadratic Riemann sums and Local integrals of $$\varvec{\zeta (s)}$$