Number Theory

    

{The Irrationality of Odd and Even Zeta Values

Authors: Timothy W. Jones

We show that using the denominators of the terms of $\zeta(n)-1=z_n$ as decimal bases gives all rational numbers in (0,1) as single decimals. We also show the partial sums of $z_n$ are not given by such single digits using the partial sum's terms. These two properties yield a proof that $z_n$ is irrational. As partials require denominators exceeding the denominators of their terms, possible single decimal convergence points are, using properties of decimal expansions, systematically eliminated.

Comments: 7 Pages. Some readers gave corrections and suggested examples.

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Submission history

[v1] 2022-04-08 03:37:24
[v2] 2022-04-16 07:58:54

Unique-IP document downloads: 401 times

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