Archiv der Mathematik (ARCH MATH )

Publisher: Mathematisches Forschungsinstitut Oberwolfach, Springer Verlag


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.

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  • Website
    Archiv der Mathematik website
  • Other titles
    Archiv der Mathematik, Archives of mathematics, Archives mathématiques
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  • Material type
    Periodical, Internet resource
  • Document type
    Journal / Magazine / Newspaper, Internet Resource

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Springer Verlag

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    • Author can archive a post-print version
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    • Authors own final version only can be archived
    • Publisher's version/PDF cannot be used
    • On author's website or institutional repository
    • On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
    • Published source must be acknowledged
    • Must link to publisher version
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    • Articles in some journals can be made Open Access on payment of additional charge
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Publications in this journal

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    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).
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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.
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    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).
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    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).
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    ABSTRACT: For one-dimensional simple symmetric random walks, we prove that the irregular set associated with the rate of returns to the origin is residual.
    Archiv der Mathematik 05/2014; 102(5).
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    ABSTRACT: In an article in the Pure and Applied Mathematics Quarterly in 2008 Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying subgroup $\Gamma_0(N)$.
    Archiv der Mathematik 04/2014; 103(1).
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    ABSTRACT: We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-$2$ class perturbation of a unitary operator. We extend this characterization from $2$ to $p$, where $2 \le p \le \infty$.
    Archiv der Mathematik 04/2014; 103(1).
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    ABSTRACT: We give necessary and sufficient conditions under which an HNN-extension with abelian base group or an amalgamated free product of abelian groups is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated). We describe HNN-extensions and amalgamated free products which are Howson groups without satisfying the Burns–Cohen statements.
    Archiv der Mathematik 04/2014; 98(2).
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    ABSTRACT: We consider classes of ideals which generalize the mixed product ideals introduced by Restuccia and Villarreal, and also generalize the expansion construction by Bayati and the first author \cite{BH}. We compute the minimal graded free resolution of generalized mixed product ideals and show that the regularity of a generalized mixed product ideal coincides with regularity of the monomial ideal by which it is induced.
    Archiv der Mathematik 03/2014; 103(1).
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    ABSTRACT: In this paper we study the vertices of indecomposable Specht modules for symmetric groups. For any given indecomposable non-projective Specht module, the main theorem of the article describes a family of p-subgroups contained in its vertex. The theorem generalizes and improves an earlier result due to Wildon in "Vertices of Specht modules and blocks of the symmetric group", J. Alg 323 (2010) 2243--2256.
    Archiv der Mathematik 03/2014; 103(1).
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    ABSTRACT: We consider the minimal Möbius invariant space of the unit disk with norm defined in terms of the second derivative. We obtain the best constant for the Bergman projection in this setting. We also show how this result generalizes to Bergman projections with respect to standard weights and beyond.
    Archiv der Mathematik 03/2014; 102(3).
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    ABSTRACT: Author’s summary: “For each finite group G, the product in the group ring of all the conjugacy class sums is a positive integer multiple of the sum of the elements in a special coset of the commutator subgroup G ' , as Brauer and Wielandt first observed in the case G ' =G. We show that the corresponding special element G! in A:=G/G ' is the product of B! over specified subgroups B of A. Somewhat analogously, the product of all the irreducible characters of G, restricted to the center Z of G, is a multiple of a special linear character !G of Z, and !G is the product of !(Z/Y) over specified subgroups Y of Z.” The author has given also very nice corollaries to his main results and instructive examples dealing with partition functions in the symmetric group S n , with the group SL 2 (q), zeros of characters. To give an example of the connecting problems and results mentioned and proved in the paper, we provide the author’s Corollaries 1 and 2 (text paraphrased) 1) Given a finite group G, then the order of the commutator subgroup of G divides the product of the cardinalities of all the conjugacy classes of G, each class considered once. 2) If each noncentral class of G is a zero for at least one irreducible character of G, then, with Z being the center of G and F being the quotient group G/Z and d being the greatest common divisor of the degrees χ(1) in Irr(G) with lie over !G (!G is a particular linear character of Z; see the paper), the order of F divides d times the product of all χ(1) with χ running through Irr(G).
    Archiv der Mathematik 03/2014; 102(3).
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    ABSTRACT: In this paper, we study a uniqueness question of entire functions sharing an entire function of smaller order with their difference operators. The results in this paper extend Theorem 1.1 in [19] by Liu and Yang and deal with Question 1 in [19], where the entire functions are of finite order. Moreover, we repair certain statements in [21] by Li et al., which in turn had depended on questionable assertions of Lemma 2.6 in [20]. Examples are provided to show that the results in this paper are best possible.
    Archiv der Mathematik 03/2014; 99(3).
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    ABSTRACT: Let D⊂ℂ n be a domain. By c D and k D we denote the pseudodistances of Carathéodory and Kobayashi, respectively. The corresponding pseudodifferential metrics will be denoted by γ D and κ D , respectively. The Lempert functional of D is denoted by l D . The author proves the following Theorem 1. Assume that n≥2. For a domain D⊂ℂ n with C 2 -boundary there exists a non-empty open set U such that c D =l D on U×U. Furthermore, there exists a non-empty open set V⊂D, such that κ D (z,X)=γ D (z,X) on V×ℂ n . The assumption n≥2 is essential for the truth of Theorem 1, as is pointed out by the author for the planar annulus A, where c A <k A everywhere. Also, as he shows by means of an example in dimension 2, the smoothness assumption on ∂D cannot be removed. He obtains an in a sense “local version” of the above theorem in strongly pseudoconvex domains, namely Theorem 2. Let D be a C 2 -smooth strongly pseudoconvex domain. Then for any z 0 ∈∂D and any neighborhood U of z 0 there is a non-empty open subset V of U×U such that c D =k D on V. Finally he shows the existence of Lempert-Burns-Krantz discs in strongly pseudoconvex domains with a C 2 -smooth boundary. Theorem 3. Let Ω be a C 2 -smoothly bounded strongly pseudoconvex domain in ℂ n . Fix p∈∂Ω. Then there exists a non-empty open subset V of Ω such that for any q∈V there exists a complex geodesic f:E⟶Ω (for c Ω ) which is Hölder-1 2 continuous on E, and such that f(1)=p, while q∈f(E). (Here E denotes the unit disc).
    Archiv der Mathematik 03/2014; 102(3).