Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series - Brevig, Ole Fredrik (MATHEMATICA SCANDINAVICA, 2016)
For a real number α the Hilbert space D_α consists of those Dirichlet series _n=1^∞ a_n/n^s for which _n=1^∞ |a_n|^2/[d(n)]^α < ∞, 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_α to the case α>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.