PreprintarXiv licencearXiv
Dynamics of multiples of zeta by exponential functions
Abstract
We study the family of functions Vz:s ↦ ζ(s) exp (zs) with numerical experiments. For selected sequences zn=xnu on rays, our experiments suggest that suitable fixed points of Vzn 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.
Related
- Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
- Representation zeta functions of self-similar branched groups
- Representation zeta functions of wreath products with finite groups
- Zeta functions of quasi-split reductive algebraic groups over local fields
- Kloosterman Sums and Plücker Height Zeta Functions
BibTeX
@misc{brent2026dynamics,
title = {{Dynamics of multiples of zeta by exponential functions}},
author = {Barry Brent},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33111},
eprint = {2609.33111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33111},
}
RIS
TY - UNPB
TI - Dynamics of multiples of zeta by exponential functions
AU - Barry Brent
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33111
UR - https://arxiv.org/abs/2609.33111
AB - We study the family of functions V_z:s ↦ 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.
ER -