Zobrazeno 1 - 10
of 122
pro vyhledávání: '"Gabriele Nebe"'
Publikováno v:
Mathematics, Vol 1, Iss 1, Pp 9-30 (2013)
Following Ramanujan’s work on modular equations and approximations of π, there are formulas for 1/π of the form [PLEASE CHECK FORMULA IN THE PDF] for d = 2, 3, 4, 6, where λd are singular values that correspond to elliptic curves with complex mu
Externí odkaz:
https://doaj.org/article/d61958a99faa4d8c860195096a2ac988
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2013 (2013)
We classify the lattices of rank 16 over the Eisenstein integers which are even unimodular -lattices (of dimension 32). There are exactly 80 unitary isometry classes.
Externí odkaz:
https://doaj.org/article/c9503845aa3643fea57b8e0c81647cf9
Autor:
Gabriele Nebe, Ghislain Fourier
Publikováno v:
Advances in Mathematics of Communications. 17:888-899
Building upon the application of flags to network coding introduced by Liebhold, Nebe, and Vazquez-Castro, we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to the space o
Autor:
Gabriele Nebe, Sihuang Hu
Publikováno v:
Journal of Number Theory. 208:262-294
We classify the dual strongly perfect lattices in dimension 16. There are four pairs of such lattices, the famous Barnes-Wall lattice $\Lambda _{16}$, the extremal 5-modular lattice $N_{16}$, the odd Barnes-Wall lattice $O_{16}$ and its dual, and one
Autor:
Gabriele Nebe, Federico Pellarin
Publikováno v:
Kyushu Journal of Mathematics. 74:401-413
Kaneko and Koike introduced the notion of extremal quasi-modular form and proposed conjectures on their arithmetic properties. The aim of this note is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The note ends with dis
Publikováno v:
Beiträge zur Algebra und Geometrie 63, 515-531 (2022). doi:10.1007/s13366-021-00600-4
We apply tropical geometry to study matrix algebras over a field with valuation. Using the shapes of min-max convexity, known as polytropes, we revisit the graduated orders introduced by Plesken and Zassenhaus. These are classified by the polytrope r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::33771e2fdc10c9848ec012710367ee3d
https://publications.rwth-aachen.de/record/834725
https://publications.rwth-aachen.de/record/834725
Autor:
Sihuang Hu, Gabriele Nebe
Publikováno v:
Journal of the London Mathematical Society. 101:1068-1089
New series of $2^{2m}$-dimensional universally strongly perfect lattices $\Lambda_I $ and $\Gamma_J $ are constructed with $$2BW_{2m} ^{\#} \subseteq \Gamma _J \subseteq BW_{2m} \subseteq \Lambda _I \subseteq BW _{2m}^{\#} .$$ The lattices are found
Autor:
Simon Eisenbarth, Gabriele Nebe
Publikováno v:
Mathematics in Computer Science. 14:443-456
In this paper, we study self-dual codes over commutative Artinian chain rings. Let R be such a ring, x be a generator of the unique maximal ideal of R and $$a\in {\mathbb {N}}_0 $$ maximal such that $$x^a\ne 0$$. A code C over R of length t is an R-s
Bolytropes are bounded subsets of an affine building that consist of all points that have distance at most $r$ from some polytrope. We prove that the points of a bolytrope describe the set of all invariant lattices of a bolytrope order, generalizing
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a887b29c6d316c36684fe985042fc875
http://arxiv.org/abs/2111.11244
http://arxiv.org/abs/2111.11244
Autor:
Gabriele Nebe, Markus Kirschmer
Publikováno v:
Experimental Mathematics. 31:280-301
In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification o...