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arxiv: 1705.06367 · v2 · pith:2P53GMBSnew · submitted 2017-05-17 · 🧮 math.NT

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

Jes\'us Guillera This is my paper
classification 🧮 math.NT
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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  1. Riemann and the logarithmic derivatives of zeta

    math.HO 2026-05 unverdicted novelty 2.0

    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.