We introduce screw functions for Dirichlet series in the extended Selberg class. Then we prove that the Grand Riemann Hypothesis for a member of the extended Selberg class is equivalent to the nonpositivity of the corresponding screw function.
Beyond the extended Selberg class: $1<d_F< 2$
On a conjecture of Erdös and certain Dirichlet series
Non-vanishing of Dirichlet series with periodic coefficients
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