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

Johan Andersson
2010 arXiv   pre-print
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
more » ... 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.
arXiv:1010.0386v1 fatcat:e3rwnxjmpnekphxsjajhflbdmi