Schlage-Puchta, Jan-Christoph
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Archiv der Mathematik

We show that an arithmetic function which satisfies some weak multiplicativity properties and in addition has a non-decreasing or log\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begi...

Yasumura, Felipe Yukihide
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Archiv der Mathematik

It was proved by Valenti and Zaicev, in 2011, that if G is an abelian group and K is an algebraically closed field of characteristic zero, then any G-grading on the algebra of upper block triangular matrices over K is isomorphic to a tensor product Mn(K)⊗UT(n1,n2,…,nd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepacka...

Datt, Gopal Kumar, Sanjay
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Archiv der Mathematik

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel’s normality test in a certain sense.

Bayer-Fluckiger, Eva Suarez, Ivan
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Archiv der Mathematik

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Becher, Karim Johannes
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Archiv der Mathematik

This note is motivated by the problem of determining the u-invariant of a field F of characteristic different from two when it is known that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...

Houriet, Julien
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Archiv der Mathematik

By a result of H.W. Lenstra, one can prove that a number field is Euclidean with the aid of exceptional units. We describe two methods computing exceptional sequences, i.e., sets of units such that the difference of any two of them is still a unit. The second method is based on a graph theory algorithm for the maximum clique problem. This yielded 4...

Bartholdi, Laurent de Cornulier, Yves
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Archiv der Mathematik

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of algebraic entropy tending to zero. All these examples are obtained by taking appropriate quotients of finitel...

Bayati, Shamila
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Archiv der Mathematik

In this paper, we show that if I is a matroidal ideal, then the ideal generated by the i-th multigraded shifts is also a matroidal ideal for every i=0,…,proj dim(I)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setleng...

Tanturri, Fabio
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Archiv der Mathematik

We prove that the Hilbert scheme of degeneracy loci of pairs of global sections of ΩPn-1(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega_{\mathbb{P}^{n-1}}^{}...

Carocca, Angel Lange, Herbert Rodríguez, Rubí E.
Published in
Archiv der Mathematik

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group...