Zeroes and rational points of analytic functions

Rational Points and Analytic Number Theory

There are a number of distinct ways in which analytic number theory can be used to provide information about rational points on algebraic varieties. Conversely, there are also a number of ways in which hoped-for results on the distribution of rational points could be used in classical problems from analytic number theory. Thus the analytic number theorist hopes not only to contribute to the the...

Fixed Points of Analytic Functions

Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions

In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class Rn,m of all rational functions of order (n,m) are considered. Let ρn,m = ρn,m( f ; E) be the distance of f in the uniform metric on E from the class Rn,m . We obtain results characterizing the rate of convergence to zero of the sequen...

A Duality in Interpolation to Analytic Functions by Rational Functions.

omission and to say whether its correction will lead only to a new interpretation of the constants of our equations or to an actual change of their form. Another simplification is the neglect of polar and excited states: While there is reason to assume that their influence is small, its exact estimate is still lacking. Further inaccuracies were discussed in our preceding paper: The use of Bloch...

On Approximation to Analytic Functions by Rational Functions

Let f(z) be analytic in the interior of a rectifiable Jordan curve C and continuous in the corresponding closed region C. The relation between continuity properties of f(z) on C and degree of approximarion to f(z) by polynomials irn(z) in z of respective degrees n, n = 1, 2, • • • , has been extensively studied. In the present paper we study the relation between continuity properties of f(z) on...