منابع مشابه
The Well-Rounded Linear Function
The generic linear function ax + b of a real variable, with a, b, x ∈ R, is usually evaluated as a scale function (product) followed by a translation (sum). Our main result shows that when such a function is variously combined with rounding functions (floor and ceiling), exactly 67 inequivalent rounded generic linear functions result, of which 38 are integer-valued and 29 are not. Several relat...
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We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of convergence at s = 1 with a real pole of order 2, improving upon a result of [11]. We use this result to show that the number of well-rounded sublattices of a planar arithmetic lattice of index less or equal N is O(N...
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We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. We consider lattices coming from full rings of integers in number fields, proving that only cyclotomic fields give rise to well-rounded lattices. We further study ...
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We prove that the well-rounded retract of SOn \ SLn R is a minimal SLn Z-invariant spine.
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(0.1). Let G be a reductive algebraic group defined over Q, and let Γ be an arithmetic subgroup of G(Q). Let X be the symmetric space for G(R), and assume X is contractible. Then the cohomology (mod torsion) of the space X/Γ is the same as the cohomology of Γ. In turn, X/Γ will have the same cohomology as W/Γ, if W is a “spine” in X . This means thatW (if it exists) is a deformation retract ofX...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2000
ISSN: 1077-8926
DOI: 10.37236/1605