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A new elementary proof of the Prime Number Theorem

Florian Karl Richter

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021

Nombre de masse

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A new elementary proof of the Prime Number Theorem

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White dwarfs as a probe of exceptionally light QCD axions

Assessment of the Lightning Performance of overhead distribution lines based on Lightning Location Systems data

Reconstruction of nerve functional topography using recruitment curves enables selective electrical stimulation

Direct observation of water-mediated single-proton transport between hBN surface defects

Charm Physics at LHCb

Oligomodal metamaterials with multifunctional mechanics

A new elementary proof of the Prime Number Theorem

Demography of galactic technosignatures

Isotope dependence of energy, momentum and particle confinement in tokamaks

Gradient expansion formalism for magnetogenesis in the kinetic coupling model