Optimal Decomposition of Odd Zeta Values: ζ(2m + 1) = α_m S_m − β_m π^(2m) / (2m + 1) and Its Arithmetic Consequences
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Veröffentlicht: |
Zenodo
2026
|
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901599551488000 |
|---|---|
| author | Olloh, Joseph |
| author_facet | Olloh, Joseph |
| contents | <p>This paper presents an elegant parity separation method to decompose odd zeta values ζ(2m+1) into an explicit rational combination of a new odd-index series S_m and a transcendental term involving π^(2m)/(2m+1). The decomposition is proved to be optimal, with the denominator 2m+1 forced by a deep divisibility property of even zeta values. The paper also establishes that S_m and ζ(2m+1) cannot both be rational, offering a fresh reduction of the irrationality problem for odd zeta values.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18354974 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Optimal Decomposition of Odd Zeta Values: ζ(2m + 1) = α_m S_m − β_m π^(2m) / (2m + 1) and Its Arithmetic Consequences Olloh, Joseph <p>This paper presents an elegant parity separation method to decompose odd zeta values ζ(2m+1) into an explicit rational combination of a new odd-index series S_m and a transcendental term involving π^(2m)/(2m+1). The decomposition is proved to be optimal, with the denominator 2m+1 forced by a deep divisibility property of even zeta values. The paper also establishes that S_m and ζ(2m+1) cannot both be rational, offering a fresh reduction of the irrationality problem for odd zeta values.</p> |
| title | Optimal Decomposition of Odd Zeta Values: ζ(2m + 1) = α_m S_m − β_m π^(2m) / (2m + 1) and Its Arithmetic Consequences |
| url | https://doi.org/10.5281/zenodo.18354974 |