Some Series Related to Extended Riemann Hypothesis for Dedekind Zeta Functions

Muhammad Atif Zaheer

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arXiv · 2512.19761

Some Series Related to Extended Riemann Hypothesis for Dedekind Zeta Functions

Muhammad Atif Zaheer

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Abstract

We obtain closed form of some infinite series involving derivatives of an analogue of the Riemann xi function for Dedekind zeta function and nontrivial zeros of Dedekind zeta function assuming the Extended Riemann Hypothesis. Conversely, we prove that if this closed form holds, then all of the zeros of Dedekind zeta function beyond a certain height lie on the critical line. This yields a large number of equivalent statements of Riemann Hypothesis.

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Muhammad Atif Zaheer. 2025-12-20. Some Series Related to Extended Riemann Hypothesis for Dedekind Zeta Functions. https://arxiv.org/abs/2512.19761

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