bibkey: danesh2026fiblucaszeta
authors: Payam Danesh
year: 2026
title: "Cancellation profiles of Fibonacci-Lucas zeta sums"
doi: null
url: https://arxiv.org/abs/2609.33564v1
claim: "The preprint analyzes cancellation and conditioning in finite Fibonacci/Lucas sums involving zeta values at negative integers; it supplies no Euler-product, Möbius, divisor-sum, or FIB-to-Robin transport theorem."
strata_touched: []
license: citation-only
triage: anchor

Cancellation profiles of Fibonacci–Lucas zeta sums

The source is Payam Danesh, arXiv:2609.33564v1, submitted 27 September 2026. It is a preprint; its proofs and numerical constants were not independently audited here, and no Lean verification is claimed.

The paper studies finite Fibonacci and Lucas weighted sums of zeta values at negative integers. For nonnegative weights of at most exponential growth it gives a finite exponential expansion for the normalized absolute-term sum, with an explicit fixed-order remainder, and proves total-variation convergence of the normalized term magnitudes to a discrete distribution determined by the even exponential generating function. In the Fibonacci and Lucas cases the limiting distribution has its unique maximum at index eight; the same index is the largest finite-sum term for every even degree at least 26. The paper also records factorial growth of the summation condition number and places the signed identities in the Bernoulli-polynomial reflection framework.

These are cancellation statements for a finite special-value sum. The zeta values occur at negative integers, and the source does not introduce the Riemann zeta Euler product, von Mangoldt coefficients, ordinary Möbius sums, or the point value

$$\frac{\sigma (N)}{N}.$$

Consequently the result cannot be substituted for a signed Robin tail or for the missing map from a FIB address to the same actual Robin candidate. The fixed cancellation profile also does not imply square-root cancellation for the ordinary Möbius function. Its use in this project is a literature boundary: it rules out treating Fibonacci–Lucas special-value cancellation as an already available RH bridge.