Abstract
A result due to Nyman establishes the equivalence of the Riemann hypothesis with the density of a set of functions in L2[0, 1]. Here a large class of analytic functions is considered, which includes the Riemann zeta function and the Dirichlet L-functions as well as functions not given by a Dirichlet series. For each such function \(\phi(s)\) there is an associated integral operator T on L2[0, 1] such that \(\phi(s)\) has no zeros in Re(s) > 1/2 iff the operator T has dense range iff a specified set of functions is dense in L2[0, 1].
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