All odd zeta values are Linearly Independent Over Q

We study the rational linear independence of the odd values of the Riemann zetafunction ζ(2n + 1) (n ≥ 1) and prove that for every positive integer n ≥ 1, the numbers1, ζ(3), ζ(5), . . . , ζ(2n + 1) are linearly independent over Q

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23881490
Primary Topic
Advanced Mathematical Identities
Type
preprint
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preprint

All odd zeta values are Linearly Independent Over Q

Prince Anand
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Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
preprint

All odd zeta values are Linearly Independent Over Q

Prince Anand
preprint en

Abstract

We study the rational linear independence of the odd values of the Riemann zetafunction ζ(2n + 1) (n ≥ 1) and prove that for every positive integer n ≥ 1, the numbers1, ζ(3), ζ(5), . . . , ζ(2n + 1) are linearly independent over Q

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
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All odd zeta values are Linearly Independent Over Q — Prince Anand · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS