The irrationality of a prime factor series under a prime tuples conjecture

2024/09/23 by Kyle Pratt, Pratt, Kyle
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2409.15185

openalex publication_date 2024/09/23 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

Let ω(n) denote the number of distinct prime factors of n. Assuming a suitably uniform version of the prime k-tuples conjecture, we show that the number ∑_n=1^∞ (ω(n))/(2ⁿ) is irrational. This settles (conditionally) a question of Erdős.

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