Sign changes in the prime number theorem

2019/10/31 by Morrill, Thomas, Platt, Dave, Trudgian, Tim
#11M06 #11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.14203

Abstract

Let V(T) denote the number of sign changes in ψ(x) - x for x∈[1, T]. We show that \liminf _T→∞ V(T)/log T ≥ γ₁/π+ 1.867⋅ 10^-30, where γ₁ = 14.13… denotes the ordinate of the lowest-lying non-trivial zero of the Riemann zeta-function. This improves on a long-standing result by Kaczorowski.

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