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Discretized Keiper/Li approach to the Riemann Hypothesis

Abstract : 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].
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Submitted on : Tuesday, January 30, 2018 - 10:23:07 AM
Last modification on : Tuesday, January 4, 2022 - 4:40:45 AM
Long-term archiving on: : Friday, May 25, 2018 - 4:21:15 PM


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



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