I have recently derived the following result: for any odd positive integer $k$, one of $\zeta(k)$ and $\zeta(k,2/3)$ is irrational.

I cannot find this result anywhere. Is it already known?

Thank you for any information.

  • $\begingroup$ I take it that by "one", you mean "at least one", rather than "exactly one". $\endgroup$ Commented Apr 10, 2022 at 23:20
  • 1
    $\begingroup$ Yes...at least one. $\endgroup$
    – rpembroke
    Commented Apr 13, 2022 at 15:39

1 Answer 1


This can be found in "On the Hurwitz Function for Rational Arguments", by V. Adamchik, https://viterbi-web.usc.edu/~adamchik/articles/AMC.pdf

  • $\begingroup$ Excellent reference $\endgroup$
    – Conrad
    Commented Apr 10, 2022 at 22:35

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