What question did this study set out to answer?

The aim is to explore the structural limits and symmetries in Diophantine approximations of zeta values, particularly for odd integers.

April 21, 2026Open Access

Structural Limits and Cyclotomic Symmetries in Diophantine Approximations of ζ(2m + 1)

Puntos clave

The aim is to explore the structural limits and symmetries in Diophantine approximations of zeta values, particularly for odd integers.
Proved a new inter-weight identity based on Ramanujan's formula.
Applied a Cyclotomic Block Theorem to analyze linear independence.
Utilized a reduction operator with Fermat-quotient chains to isolate cyclotomic factors.
Established a new identity involving β coefficients that relates to zeta values.
Shown that the zeta function cannot be isolated over rational numbers.
Clarified the differences between reductive and additive Diophantine operators.

Resumen

We prove a new inter-weight identity β₃−42β₅+315β₇=0 for the rational kernel of Ramanujan's formula for ζ(2m+1), arising from cyclotomic factorization. A Cyclotomic Block Theorem determines ℚ-linear independence across weights. A reduction operator via Fermat-quotient chains isolates cyclotomic factors and shows chronic underdetermination: ζ(s) cannot be isolated over ℚ. This demarcates reductive vs. additive Diophantine operators, explaining structural limits of modular-Lambert methods. Three obstruction results close spectral approaches.

Leer artículo completoexternamente

Me gusta

Guardar

Ver artículo completo

Cite This Study

Ricardo Hernandez Reveles (Sun,) studied this question.

synapsesocial.com/papers/69e713decb99343efc98d360 https://doi.org/https://doi.org/10.5281/zenodo.19422992

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Me gusta

Guardar

Ver artículo completo