遇见数据集

A Certified Census of Davenport-Heilbronn Zeros to Height 20,000

收藏
Zenodo2026-08-12 更新2026-08-13 收录
官方服务:

资源简介:

Certified catalog of 1,233 off-line zero pairs of the Davenport-Heilbronnfunction D(s) below height t = 20,000 -- to our knowledge the first largeenumeration of off-line zeros for the classical 1936 counterexample thatsatisfies a Riemann-type functional equation while violating the RHanalogue (prior literature: a handful of zeros, Spira 1994 andBalanzario-Sanchez-Ortiz 2007). Highlights: complete census closure below t = 1,000 (848 on-line + 56off-line = 904 zeros, matching the von Mangoldt count exactly);argument-principle winding certificate for every off-line pair; matchedcontrol design using the component L(s,chi), chi the odd quartic charactermod 5; a theorem draft showing integer moments are structurally blind tothe violation; a pre-registration ledger including failed predictions. Contents: certified zero catalog (CSV with per-row residual, winding, andprovenance), adjudication campaign code (Python: mpmath/numpy/scipy),critical-line value tables, three-page results memo, paper skeleton, and aREADME with a ten-second-to-days reproduction ladder. Computed with AI assistance (Anthropic Claude) in numerics, theoremdrafting, and campaign design; every numerical claim is independentlyreproducible from this package without any AI involvement.

提供机构:
Zenodo
创建时间:
2026-08-12
二维码
社区交流群
二维码
科研交流群
商业服务