Ijtihed Kilani

On the irrationality of 2-adic zeta values in short intervals

We prove that, for every odd integer s ≥ 7, there exists an odd integer j in the interval [s, 1.7s) such that the Kubota–Leopoldt 2-adic zeta value \(\zeta_2(j)\) is irrational. This shortens the interval [s+3, 3s+5] of Lai. In particular, ζ₂(7) is irrational (a new proof), at le...