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arXiv · 1104.3617

Asymptotic harmonic behavior in the prime number distribution

Maurice H. P. M. van Putten
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Abstract

We consider $\Phi(x)=x^{-\frac{1}{4}}\left[1-2\sqrt{x}\Sigma e^{-p^2\pi x}\ln p\right]$ on $x>0$, where the sum is over all primes $p$. If $\Phi$ is bounded on $x>0$, then the Riemann hypothesis is true or there are infinitely many zeros Re~$z_k>\frac{1}{2}$. The first 21 zeros give rise to asymptotic harmonic behavior in $\Phi(x)$ defined by the prime numbers up to one trillion.

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Maurice H. P. M. van Putten. 2011-04-19. Asymptotic harmonic behavior in the prime number distribution. https://arxiv.org/abs/1104.3617

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