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

· 2017 · math.NT · arXiv 1705.06367

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abstract

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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math.HO 1

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2026 1

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UNVERDICTED 1

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Riemann and the logarithmic derivatives of zeta

math.HO · 2026-05-26 · 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.

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  • Riemann and the logarithmic derivatives of zeta math.HO · 2026-05-26 · unverdicted · none · ref 5 · internal anchor

    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.