The Mangoldt function and the non-trivial zeros of the Riemann zeta function

Jes\'us Guillera

The Mangoldt function and the non-trivial zeros of the Riemann zeta function

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arxiv 1705.06367 v2 pith:2P53GMBS submitted 2017-05-17 math.NT

Jesús Guillera This is my paper · ORCID

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keywords functionmangoldtnon-trivialriemannzeroszetaadditionanalize

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We prove a formula for the Mangoldt function which relates it to a sum over all the non-trivial zeros of the Riemann zeta function, in addition we analize a truncated version of it.

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Riemann and the logarithmic derivatives of zeta
math.HO 2026-05 unverdicted novelty 2.0 of 10

Riemann supplied explicit values for the derivatives of log ζ(s) at s=1/2, including ζ'(1/2)/ζ(1/2) = π/4 + γ/2 + log(8π)/2 and a second-derivative formula 8 - π²/4 - 2G + 2 ∑ 1/α_n².

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