
TL;DR
This paper investigates the Laurent series expansion of the inverse zeta function at nontrivial zeros and explores its implications for the zeros' simplicity, contributing to understanding the Riemann zeta function's zeros.
Contribution
It provides a novel analysis of the Laurent series of 1/ζ(s) at zeros to study the simplicity of these zeros, linking series properties to zero multiplicity.
Findings
Laurent series of 1/ζ(s) at zeros reveals zero simplicity
Connection established between series behavior and zero multiplicity
Insights potentially inform the Riemann Hypothesis
Abstract
This note studies the Laurent series of the inverse zeta function at any fixed nontrivial zero of the zeta function , and its connection to the simplicity of the nontrivial zeros.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Mathematical Theories
