An Explicit Error Bound O((log n)^{-7}) with Constant C = 18 for the Riemann Zeros – Verified for the First Million Terms

This dataset contains: - 1 000 000 computed Riemann zeros (γ_n) using the Zampaglione v6.0 formula- Exact values from mpmath.zetazero(n) for comparison- Absolute error for each n- Theoretical bound 18/(log n)^7 for n ≥ 100 The maximum observed error is 2.15 × 10^{-10} at n = 1 000 000.The bound C = 18 is analytically proven and verified for all n ≥ 100. Paper: https://arxiv.org/abs/2512.06987Code: https://github.com/zampaglione/riemann-zeros-bound Author: Fortunato Zampaglione – Independent researcher, Monza, ItalyDate: 10 December 2025

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-12-11
DOI
https://doi.org/10.5281/zenodo.17888299
Primary Topic
Analytic Number Theory Research
Type
article
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article

An Explicit Error Bound O((log n)^{-7}) with Constant C = 18 for the Riemann Zeros – Verified for the First Million Terms

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

An Explicit Error Bound O((log n)^{-7}) with Constant C = 18 for the Riemann Zeros – Verified for the First Million Terms

article en

Abstract

This dataset contains: - 1 000 000 computed Riemann zeros (γ_n) using the Zampaglione v6.0 formula- Exact values from mpmath.zetazero(n) for comparison- Absolute error for each n- Theoretical bound 18/(log n)^7 for n ≥ 100 The maximum observed error is 2.15 × 10^{-10} at n = 1 000 000.The bound C = 18 is analytically proven and verified for all n ≥ 100. Paper: https://arxiv.org/abs/2512.06987Code: https://github.com/zampaglione/riemann-zeros-bound Author: Fortunato Zampaglione – Independent researcher, Monza, ItalyDate: 10 December 2025

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 21%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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An Explicit Error Bound O((log n)^{-7}) with Constant C = 18 for the Riemann Zeros – Verified for the First Million Terms · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS