Concept

Décomposition en produit de facteurs premiers

Publications associées (110)

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ELSEVIER2021

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

A decomposition of multicorrelation sequences for commuting transformations along primes

Florian Karl Richter

A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer

k

and every

\delta>0

there exists

n

such that every subset of ${1, ...

2021

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A decomposition of multicorrelation sequences for commuting transformations along primes

Florian Karl Richter

A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer

k

and every

\delta>0

there exists

n

such that every subset of ${1, ...

2021

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