In mathematics, the Hermite constant, named after Charles Hermite, determines how long a shortest element of a lattice in Euclidean space can be.
The constant γn for integers n > 0 is defined as follows. For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let λ1(L) denote the least length of a nonzero element of L. Then √γn is the maximum of λ1(L) over all such lattices L.
The square root in the definition of the Hermite constant is a matter of historical convention.
Alternatively, the Hermite constant γn can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume.
the Hermiteconstant, named after Charles Hermite, determines how long a shortest element of a lattice in Euclidean space can be. The constant γn for...
Eric W. "Soldner's Constant". MathWorld. Weisstein, Eric W. "Gauss's Constant". MathWorld. Weisstein, Eric W. "HermiteConstants". MathWorld. Weisstein...
transcendental numbers Hermiteconstant, a constant related to the geometry of certain lattices Hermite-Gaussian modes The Hermite–Hadamard inequality on...
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...
analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is...
functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his...
solutions of the paraxial Helmholtz equation can be decomposed as the sum of Hermite–Gaussian modes (whose amplitude profiles are separable in x and y using...
Close-packing of equal spheres Apollonian sphere packing Finite sphere packing Hermiteconstant Inscribed sphere Kissing number Sphere-packing bound Random close pack...
of Hermite class. Since a non-constant function of Hermite class is the limit of a sequence of such polynomials, its derivative will be of Hermite class...
320^{3}+744.} This number was discovered in 1859 by the mathematician Charles Hermite. In a 1975 April Fool article in Scientific American magazine, "Mathematical...
implementations of these algorithms are also listed. Nguyen, Phong Q. (2009). "Hermite'sConstant and Lattice Algorithms". The LLL Algorithm. Information Security and...
In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count...
denominator, yet Hermite could make R(r) too small to have such a denominator, hence a contradiction. To prove that e was in fact transcendental, Hermite took his...
{vol} _{n}(M),} where γ n {\displaystyle \gamma _{n}} is the classical Hermiteconstant. Asymptotic phenomena for the systole of surfaces of large genus have...
analog of Jensen-Franel's formula for the generalized Stieltjes constant is the Hermite formula γ n ( a ) = [ 1 2 a − ln a n + 1 ] ( ln a ) n − i ∫...
Global Information