ZEROS OF FUNCTIONS IN BERGMAN-TYPE HILBERT SPACES OF DIRICHLET SERIES

摘要

For a real number a the Hilbert space D-alpha consists of those Dirichlet series Sigma(infinity)(n=1) a(n)(s) for which Sigma(infinity)(n=1) |a(n)|(2)/[d(n)](alpha) < infinity, where d(n) denotes the number of divisors of n. We extend a theorem of Seip on the bounded zero sequences of functions in D-alpha to the case alpha > 0. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series H-P, for 1 <= p < 2.