Lavrentiev's approximation theorem with nonvanishing polynomials and universality of zeta-functions

Details Lavrentiev's approximation theorem with nonvanishing polynomials and universality of zeta-functions Lavrentiev's approximation theorem with nonvanishing polynomials and universality of zeta-functions

2010-10-03

arxiv.org/abs/1010.0386v1

Directions in Value-distribution Theory of Zeta and L-functions: Wurzburg Conference, October 6-10, 2008 (Berichte aus der Mat

Mathematics

Number Theory

5 pages

Scientific paper

We prove a variant of the Lavrentiev's approximation theorem that allows us to approximate a continuous function on a compact set K in C without interior points and with connected complement, with polynomial functions that are nonvanishing on K. We use this result to obtain a version of the Voronin universality theorem for compact sets K, without interior points and with connected complement where it is sufficient that the function is continuous on K and the condition that it is nonvanishing can be removed. This implies a special case of a criterion of Bagchi, which in the general case has been proven to be equivalent to the Riemann hypothesis.

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