Year: 2026
Type: preprint
Abstract: We study the family of functions $V_z:s \mapsto ζ(s) \exp (zs)$ with numerical experiments. For selected sequences $z_n=x_nu$ on rays, our experiments suggest that suitable fixed points of $V_{z_n}$ approach nontrivial zeros of $ζ$ in a nearly logarithmic pattern. We formulate this behavior as conjectures with explicit restrictions on the ray. We prove a conditional result identifying finite limits as zeros, and give sufficient hypotheses for the convergence of refinement diagnostics. Substantive AI assistance in the preparation of this draft is disclosed in Section 5.
Source: arXiv (Cornell University)
Author: Brent, Barry
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214796049