Shells of Selfdual Lattices Viewed as Spherical Designs
نویسنده
چکیده
We find out for which t shells of selfdual lattices and of theirs shadows are spherical t-designs. The method uses theta series of lattices, which are modular forms. We analyse fully cubic and Witt lattices, as well as all selfdual lattices of rank at most 24.
منابع مشابه
Spherical Designs from 3 Norm Shell of Integral Lattices
A set of vectors all of which have a constant (non-zero) norm value in a Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Rèseuaux et “designs” sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.
متن کاملSpherical Designs from Norm-3 Shell of Integral Lattices
A set of vectors all of which have a constant (non-zero) norm value in an Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Réseaux et “designs” sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.
متن کاملBoris Venkov’s Theory of Lattices and Spherical Designs
Boris Venkov passed away on November 10, 2011, just 5 days before his 77th birthday. His death overshadowed the conference “Diophantine methods, lattices, and arithmetic theory of quadratic forms” November 13-18, 2011, at the BIRS in Banff (Canada), where his important contributions to the theory of lattices, modular forms and spherical designs played a central role. This article gives a short ...
متن کاملNew Complex- and Quaternion-hyperbolic Reflection Groups
We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite index. These provide new finitecovolume reflection groups acting on complex and quaternionic hyperbolic spaces. Specifically, we provide groups acting on CH for all n < 6 and n = 7, and on HH for n = 1, 2, 3, and 5. We co...
متن کاملSpherical Designs and Zeta Functions of Lattices
We set up a connection between the theory of spherical designs and the question of minima of Epstein’s zeta function. More precisely, we prove that a Euclidean lattice, all layers of which hold a 4-design, achieves a local minimum of the Epstein’s zeta function, at least at any real s > n 2 . We deduce from this a new proof of Sarnak and Strömbergsson’s theorem asserting that the root lattices ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IJAC
دوره 15 شماره
صفحات -
تاریخ انتشار 2005