# Archiv der Mathematik (ARCH MATH )

## Description

Archiv der Mathematik publishes original contributions preferably not longer than 10 printed pages from the entire field of mathematics and its applications which are of interest to a large readership. Short but comprehensive authors' summaries of longer works which are not yet published as well as limited number of survey articles are also published. The journal is well known for its emphasis on papers dealing with solutions of problems in classical and modern mathematics which are not overly technical in nature.

- Impact factor0.38Show impact factor historyImpact factorYear
- 5-year impact0.44
- Cited half-life0.00
- Immediacy index0.02
- Eigenfactor0.01
- Article influence0.45
- WebsiteArchiv der Mathematik website
- Other titlesArchiv der Mathematik, Archives of mathematics, Archives mathématiques
- ISSN0003-889X
- OCLC1481903
- Material typePeriodical, Internet resource
- Document typeJournal / Magazine / Newspaper, Internet Resource

## Publisher details

- Pre-print
- Author can archive a pre-print version

- Post-print
- Author can archive a post-print version

- Conditions
- Author's pre-print on pre-print servers such as arXiv.org
- Author's post-print on author's personal website immediately
- Author's post-print on any open access repository after 12 months after publication
- Publisher's version/PDF cannot be used
- Published source must be acknowledged
- Must link to publisher version
- Set phrase to accompany link to published version (see policy)
- Articles in some journals can be made Open Access on payment of additional charge

- Classification green

## Publications in this journal

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**ABSTRACT:**In this short note, we provide a simple proof of Hardy’s inequality in a limiting case. In the proof we do not need any symmetrization technique such as the Polya–Szegö inequality for the spherical decreasing rearrangement.Archiv der Mathematik 12/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this note, we show that if a finite group G has only one conjugacy class of subgroups of an odd prime order p, then G has a p-block of defect zero if and only if O p (G) = 1. Generally, this result is not true for p even. However, we show that it is true if G does not have quotient groups isomorphic to M 22 or A 7.Archiv der Mathematik 12/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Let $f(z)=\sum_{n=1}^\infty a(n)e^{2\pi i nz}\in S_k^{new}(\Gamma_0(N))$ be a newform of even weight $k\geq2$ that does not have complex multiplication. Then $a(n)\in\mathbb{R}$ for all $n$, so for any prime $p$, there exists $\theta_p\in[0,\pi]$ such that $a(p)=2p^{(k-1)/2}\cos(\theta_p)$. Let $\pi(x)=\#\{p\leq x\}$. For a given subinterval $I\subset[0,\pi]$, the now-proven Sato-Tate Conjecture tells us that as $x\to\infty$, \[ \#\{p\leq x:\theta_p\in I\}\sim \mu_{ST}(I)\pi(x),\quad \mu_{ST}(I)=\int_{I} \frac{2}{\pi}\sin^2(\theta)~d\theta. \] Let $\epsilon>0$. Assuming that the symmetric power $L$-functions of $f$ are automorphic, we prove that as $x\to\infty$, \[ \#\{p\leq x:\theta_p\in I\}=\mu_{ST}(I)\pi(x)+O\left(\frac{x}{(\log x)^{9/8-\epsilon}}\right), \] where the implied constant is effectively computable and depends only on $k,N,$ and $\epsilon$.Archiv der Mathematik 07/2014; 103(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**We bound the order of a finite p-group in terms of its exponent and p-rank. Here the p-rank is the maximal rank of an abelian subgroup. These results are applied to defect groups of p-blocks of finite groups with given Loewy length. Doing so, we improve results in a recent paper by Koshitani, Külshammer, and Sambale. In particular, we determine possible defect groups for blocks with Loewy length 4.Archiv der Mathematik 07/2014; 103(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**Let N≥5 and D 2,2 (ℝ N ) denote the closure of C 0 ∞ (ℝ N ) in the norm ∥u∥ D 2,2 (ℝ N ) 2 :=∫ ℝ N |Δu| 2 . Let K∈C 2 (ℝ N ). We consider the following problem for ε≥0: (P ε )Findu∈D 2,2 (ℝ N )solving:Δ 2 u=(1+εK(x))u N+4 N-4 inℝ N u>0inℝ N · We show an exact multiplicity result for (P ε ) for all small ε>0.Archiv der Mathematik 06/2014; 102(6). - Archiv der Mathematik 06/2014; 102(6).
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**ABSTRACT:**Let G be a finite group and m a natural number. The twisting function with m variables on G is defined by τ m (x 1 ,...,x m ):=(x 1 x 2 ,...,x m-1 x m ,x m x 1 ) and has been introduced and studied by the third author in [5]. In the current paper, we extend and sharpen results from Kaplan (see [5]) on solvability and nilpotency (see Theorems 1.2 and 1.1). Furthermore, for groups G such that τ 2 is a permutation on the cartesian product G 2 , we investigate the order of this permutation and its connection to properties of G.Archiv der Mathematik 06/2014; 102(6). - [Show abstract] [Hide abstract]

**ABSTRACT:**The topological data of a group action on a compact Riemann surface can be encoded using a tuple (h;m 1 ,...,m s ) called its signature. There are two number theoretic conditions on a tuple necessary for it to be a signature: the Riemann-Hurwitz formula is satisfied and each m i equals the order of a non-trivial group element. We show on the genus spectrum of a group that asymptotically, satisfaction of these conditions is in fact sufficient. We also describe the order of growth for the number of tuples which satisfy these conditions but are not signatures in the case of cyclic groups.Archiv der Mathematik 06/2014; 102(6). -
##### Article: Dead-core rates for the fast diffusion equation with a spatially dependent strong absorption

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**ABSTRACT:**This paper deals with the dead-core rates problem for the fast diffusion equation with a spatially dependent strong absorption. where 0<p<m<1and−1<q<0. By using the self-similar transformation technique and the Zelenyak method, we proved that the temporal dead-core rate is non-self-similar.Archiv der Mathematik 05/2014; 102(2014):469–481. - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commutators are covered by m procyclic subgroups, then G possesses a finite characteristic subgroup M contained in G' such that the order of M is m-bounded and G'/M is procyclic. If G is a pro-p group such that all commutators in G are covered by m procyclic subgroups, then G' is either finite of m-bounded order or procyclic.Archiv der Mathematik 05/2014; 103(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**Let R be a polynomial ring over ${\mathbb{C}}$. In this paper we show that a polynomial in R [3] is a residual coordinate if and only if it is a stable coordinate.Archiv der Mathematik 05/2014; 100(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**We determine the set of primitive integral solutions to the generalised Fermat equation x 2 +y 3 =z 15 . As expected, the only solutions are the trivial ones with xyz=0 and the non-trivial one (x,y,z)=(±3,-2,1).Archiv der Mathematik 05/2014; 102(5). - [Show abstract] [Hide abstract]

**ABSTRACT:**We give a non-probabilistic proof for the boundary integral representation of μ-harmonic functions on topological semigroups.Archiv der Mathematik 05/2014; 102(5).

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.