A simple inequality relating the Euler-Riemann zeta function, digamma, and cotangent over the unit interval

Michael Andrew Henry

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arXiv · 2601.00631

A simple inequality relating the Euler-Riemann zeta function, digamma, and cotangent over the unit interval

Michael Andrew Henry

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Abstract

We prove an inequality featuring three well-known functions from analysis, namely the cotangent, the Euler-Riemann zeta function, and the digamma function. Aside from a simple proof of our result, we give a conjectured strengthening. We offer various remarks about the origins of this problem.

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Michael Andrew Henry. 2026-01-02. A simple inequality relating the Euler-Riemann zeta function, digamma, and cotangent over the unit interval. https://arxiv.org/abs/2601.00631

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