Dimensions of some affine Deligne–Lusztig varieties
Dimensions of spaces of cusp forms over function fields.
Dimensions of spaces of modular forms for
Diophantine Analysis Applied to Virus Structure.
Diophantine approximation and certain sequences of lattices
Diophantine approximation and deformation
Diophantine Approximation and Lattices with Complex Multiplication.
Diophantine approximation and special Liouville numbers
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers . The approach relies on results on the connection between the set of all -adic expansions () of and their associated approximation constants. As an application, explicit construction of real numbers with prescribed approximation properties are deduced and illustrated by Matlab plots.
Diophantine approximation by square-free numbers
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Diophantine approximation in Banach spaces
In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
Diophantine Approximation in certain Solenoids
Diophantine Approximation in Characteristic p.
Diophantine approximation in power series fields
Diophantine approximation in short intervals
Diophantine approximation involving primes.
Diophantine Approximation on Abelian Varieties with Complex Mulitplication.
Diophantine approximation on affine hyperplanes
Diophantine approximation on algebraic varieties
We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.
Diophantine approximation on Veech surfaces
We show that Y. Cheung’s general -continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an appropriate sense. The saddle connection continued fractions then allow one to recognize certain transcendental...