The Chenian Weighting System: An Algebraic Unification of Continuous Power Sums and Riemann Zeta Values
Abstract
We present a self-contained algebraic framework, the Chenian Weighting System (CWS), for solving the closed-form expression of continuous integer power sums S_k(N) and their analytic continuation to \zeta(-k). By defining a set of dynamic weight operators W_j, we derive a summation formula applicable to all positive integers k and establish a rigorous mapping between Chenian weights and Bernoulli constants. This study details the polynomial basis construction of S_k(N) and explains the trivial zeros of the Riemann Zeta function through algebraic symmetry breaking.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Mathematical functions and polynomials
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 6 March 2026
- Language
- EN
- Document type
- Preprint