Strong approximation in the Apollonian group

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Strong Approximation in the Apollonian Group

The Apollonian group is a finitely generated, infinite index subgroup of the orthogonal group OQ(Z) fixing the Descartes quadratic form Q. For nonzero v ∈ Z4 satisfying Q(v) = 0, the orbits Pv = Av correspond to Apollonian circle packings in which every circle has integer curvature. In this paper, we specify the reduction of primitive orbits Pv mod any integer d > 1. We show that this reduction...

متن کامل

Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...

متن کامل

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

A Descartes configuration is a set of four mutually tangent circles in the Riemann sphere, having disjoint interiors. Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. Part I shoewed there is a natural group action on Desc...

متن کامل

Strong approximation methods in group theory LMS/EPSRC Short course

Here ZS = Z[1/p | p ∈ S]. In case (b) we can deduce from the Strong Approximation Theorem that ∆1 has many finite images, in particular the groups ∏k i=1 G(Fpi) whenever p1, . . . , pk are distinct primes outside S. Now, for all but finitely many primes p the group G(Fp) is semisimple, in fact it is a perfect central extension of a product of simple groups (of fixed Lie type over Fp). The simpl...

متن کامل

Apollonian Circle Packings : Geometry and Group Theory

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2011

ISSN: 0022-314X

DOI: 10.1016/j.jnt.2011.05.010