Eisenstein Integers and Related C-groups
نویسنده
چکیده
Using modular quotients of linear groups deened over the Eisenstein ring Z!], we construct innnite families of nite regular or chiral polytopes of types f3; 3; 6g, f3; 6; 3g and f6; 3; 6g.
منابع مشابه
EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...
متن کاملThe Leech Lattice and Complex Hyperbolic Re ections
We construct a natural sequence of nite-covolume reeection groups acting on the complex hy-perbolic spaces C H 13 , C H 9 and C H 5 , and show that the 9-dimensional example coincides with the largest of the groups of Mostow 10]. These reeection groups arise as automorphism groups of certain Lorentzian lattices over the Eisenstein integers, and we obtain our largest example by using the complex...
متن کاملNew complex and quaternion-hyperbolic re ection groups
We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we nd reeection groups of nite index. These provide explicit constructions of new nite-covolume reeection groups acting on complex and quaternionic hyperbolic spaces of high dimensions. Speciically, we provide groups acting on C H n for all n < 6 and n = 7,...
متن کاملEven Powers of Divisors and Elliptic Zeta Values
We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann’s zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisor...
متن کاملLehmer's Conjecture for Hermitian Matrices over the Eisenstein and Gaussian Integers
We solve Lehmer’s problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least Lehmer’s number τ0 = 1.17628 . . . .
متن کامل