Discretized Keiper/Li approach to the Riemann Hypothesis

André Voros (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

The Keiper–Li sequence {$\lambda_n$} is most sensitive to the Riemann Hypothesis asymptotically ($n \rightarrow \infty$), but highly elusive both analytically and numerically. We deform it to fully explicit sequences, simpler to analyze and to compute (up to $n$ = 5·10$^5$ by G. Misguich). We extend that to the Davenport–Heilbronn counterexamples, then demonstrate explicit tests that selectively react to zeros $off$ the critical line. The present text develops our computations announced from 2015 [34].

Keywords: Keiper-Li sequence; Li's criterion; Riemann Hypothesis; Riemann zeros; steepest-descent method; Dirichlet L-functions; Davenport-Heilbronn functions

Domains: Physics [physics]

André Voros. Discretized Keiper/Li approach to the Riemann Hypothesis. Experimental Mathematics, 2018, ⟨10.1080/10586458.2018.1482480⟩. ⟨cea-01696126⟩