17 research outputs found
Bounding basis reduction properties
The paper describes improved analysis techniques for basis reduction
that allow one to prove strong complexity bounds and reduced basis
guarantees for traditional reduction algorithms and some of their
variants. This is achieved by a careful exploitation of the linear
equations and inequalities relating various bit sizes before and after
one or more reduction steps
QUARTIC DOUBLE SOLIDS WITH ICOSAHEDRAL SYMMETRY
We study quartic double solids admitting icosahedral symmetry.Comment: 19 page
Badly approximable points on manifolds
Addressing a problem of Davenport we show that any finite intersection of the sets of weighted badly approximable points on any analytic nondegenerate manifold in has full dimension. This also extends Schmidt's conjecture on badly approximable points to arbitrary dimensions