On the Sum of Reciprocals of Primes

2024/01/06 by Young Deuk Kim, Kim, Young Deuk
Mathematics · #11N05 #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.04768

openalex publication_date 2024/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that y>0, 0≤α<2π, and 0K and P^- the set of primes p such that cos(yln p+α)<-K. In this paper, we prove ∑_{p∈ P⁺}(1)/(p)=∞ and ∑_{p∈ P^-}(1)/(p)=∞.

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