Affiliation:
1. Department of Mathematics and Computer Science St Petersburg State University Saint Petersburg Russia
Abstract
AbstractWe show that the analytic continuations of Helson zeta functions can have essentially arbitrary poles and zeroes in the strip (unconditionally), and in the whole critical strip under Riemann Hypothesis, with the function taking values in cubic roots of unity. If the sets of zeroes and poles are symmetric with respect to the real axis, the same can be achieved with taking values . The proof is constructive.