Simultaneous Diophantine Approximation on Polynomial Curves

The Hausdorff dimension and measure of the set of simultaneously ψ-approximable points lying on integer polynomial curves is obtained for sufficiently small error functions

New estimates for the number of integer polynomials with given discriminants

In this paper, we propose a new method of upper bounds for the number of integer polynomials of the fourth degree with a given discriminant. By direct calculation similar results were established by H. Davenport and D. Kaliada for polynomials of second and third degrees

Discriminants of polynomials in the Archimedean and non-Archimedean metrics

An upper bound for the number of cubic polynomials which have small discriminant in terms of the Euclidean and p-adic metrics simultaneously is obtained

Simultaneous Diophantine approximation of integral polynomials in the different metrics

There is no abstract available for this article

On the Number of Polynomials with Small Discriminants in the Euclidean and p-adic Metrics

In this article it is proved that there exist a large number of polynomials which have small discriminant in terms of the Euclidean and p-adic metrics simultaneously. The measure of the set of points which satisfy certain polynomial a nd derivative conditions is also determine

Simultaneous Diophantine approximation of integral polynomials in the different metrics

There is no abstract available for this article

Simultaneous Diophantine approximation of integral polynomials in the different metrics

There is no abstract available for this article

Diophantine approximation on non‐degenerate curves with non‐monotonic error function

It is shown that a non‐degenerate curve in ℝn satisfies a convergent Groshev theorem with a non‐monotonic error function. In other words it is shown that if a volume sum converges the set of points lying on the curve which satisfy a Diophantine condition has Lebesgue measure zero