Some series equivalent to the extended Riemann hypothesis for Dedekind zeta functions (2509.21518v1)

Abstract: The extended Riemann hypothesis (ERH) for Dedekind zeta functions remains one of the most elusive open problems in number theory. Over the last century, many equivalent statements to the classical Riemann hypothesis alone have been discovered. We seek to show that the closed form of some infinite series over the non-trivial zeros of Dedekind zeta functions is equivalent to ERH.