The taper and the gain: twelve bands of the ladder

The runner walks from one zero to the next. To do it, it listens to a bank of tones built from the primes, and the sum of those tones is the wobble that says how far the next zero has drifted from where the smooth count puts it. Three things about that listening were measured here, on twelve stretches of the ladder running from height seventy-seven thousand up to three thousand three hundred million. Every stretch is six thousand consecutive zeros the runner found for itself. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23848995
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

The taper and the gain: twelve bands of the ladder

James Norman Ibbotson
2 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

The taper and the gain: twelve bands of the ladder

James Norman Ibbotson
preprint en

Abstract

The runner walks from one zero to the next. To do it, it listens to a bank of tones built from the primes, and the sum of those tones is the wobble that says how far the next zero has drifted from where the smooth count puts it. Three things about that listening were measured here, on twelve stretches of the ladder running from height seventy-seven thousand up to three thousand three hundred million. Every stretch is six thousand consecutive zeros the runner found for itself. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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The taper and the gain: twelve bands of the ladder — James Norman Ibbotson · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS