A way to prove the irrationality of Zeta(4)

2014/06/13 by Huylebrouck, Dirk
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1406.4464

Abstract

The proof of the irrationality of Zeta(5) is a long standing open problem, but here only the case of Zeta(4) = (Pi⁴)/90 is considered. The present paper suggests an approach for the irrationality of Zeta(4) along the lines of those known for proving the irrationality of Zeta(3).

Related

• ζ(5) is irrational
• A note on the irrationality of ζ₂(5)
• A note on the Irrationality of ζ(5) and Higher Odd Zeta Values
• A Note on a Recent Attempt to Prove the Irrationality of ζ(5)
• Infinitely many odd zeta values are irrational. By elementary means