Number Theory

On Fauzan’s Proof that ζ(5) is Irrational

Authors: Chun Wing Lai

We present a corrected and expanded version of A. Fauzan’s 2026 Zenodo preprint ζ(5) is irrational. The mathematical argument is Fauzan’s: it constructs a family of integer polynomials Q_n satisfying 0 < Q_n(ζ(5)) <e^(−cn^2) as Hankel determinants of a rational functional, using a positive moment representation and a logarithmic energy estimate. Our contribution is to supply detailedderivations for several steps that the preprint states without proof, to correct a typographical error in the definition of an auxiliary functional, to correct four decimal-point typos in the final numerical constants, and to document two expositional defects in Section 5 that do not affect the final conclusion. The proof is written to be accessible to advanced undergraduates.

Comments: 19 Pages.

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Submission history

[v1] 2026-09-29 20:34:57

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