On the Sum of Reciprocals of Primes

Young Deuk Kim

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arXiv · 2403.04768

On the Sum of Reciprocals of Primes

Young Deuk Kim

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Abstract

Suppose that $y>0$, $0\leq\alpha<2\pi$, and $0 K$ and $P^-$ the set of primes $p$ such that $\cos(y\ln p+\alpha)<-K$. In this paper, we prove $\sum_{p\in P^+}\frac{1}{p}=\infty$ and $\sum_{p\in P^-}\frac{1}{p}=\infty$.

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Young Deuk Kim. 2024-01-06. On the Sum of Reciprocals of Primes. https://arxiv.org/abs/2403.04768

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