On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019/04/05 by WonTae Hwang, Hwang, WonTae, Kyunghwan Song +1
Mathematics · Physics and Astronomy · #11B83 #11G30 #11M06 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1904.03060

openalex publication_date 2019/04/05 · openalex created_date 2019/04/11 · openalex updated_date 2026/07/28

Abstract

We prove that the integer part of the reciprocal of the tail of ζ(s) at a rational number s=(1)/(p) for any integer with p ≥ 5 or s=(2)/(p) for any odd integer with p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when s=(2)/(p), we use a result on the finiteness of integral points of certain curves over ℚ.

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