A remark on rational approximation

A Remark on Approximation on Totally Real Sets

We give a new proof of a theorem on approximation of continuous functions on totally real sets.

A remark on the rational cohomology of S1,n

We focus on the rational cohomology of Cornalba’s moduli space of spin curves of genus 1 with n marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes.

A Note on Approximation by Rational Functions

The theory of the approximation by rational functions on point sets E of the js-plane (z = x+iy) has been summarized by J. L. Walsh who himself has proved a great number of important theorems some of which are fundamental. The results concern both the case when E is bounded and when E extends to infinity. In the present note a Z^-theory (0<p< oo) will be given for the following point sets exten...

Diophantine approximation on rational quadrics

We compute the Hausdorff dimension of sets of very well approximable vectors on rational quadrics. We use ubiquitous systems and the geometry of locally symmetric spaces. As a byproduct we obtain the Hausdorff dimension of the set of rays with a fixed maximal singular direction, which move away into one end of a locally symmetric space at linear depth, infinitely many times.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem