Some series equivalent to the extended Riemann hypothesis for Dedekind zeta functions

2025/09/25 by Nguyen, Vincent · 1 citation
#11M26 #11R42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.21518

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 prove that the closed form of some infinite series over the non-trivial zeros of Dedekind zeta functions holds if and only if ERH is true.

Citations

• Transcendental sums related to the zeros of zeta functions

Cited by

• Some Series Related to Extended Riemann Hypothesis for Dedekind Zeta Functions

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