PreprintCC BY 4.0arXiv
Finite Rodriguez-Villegas Approximants to the Riemann ξ-Function
Abstract
We construct a sequence of finite Rodriguez-Villegas transforms converging locally uniformly to the Riemann ξ-function in the critical strip. The input is a positive symmetric profile on the unit interval obtained from the Riemann theta kernel through convolution with the hyperbolic-secant kernel and the logistic coordinate. The profile is a Stieltjes function of x(1−x). Its Bernstein polynomials produce reciprocal numerators and exact finite functional equations. The same numerators admit an exact realization as fermionic supertraces, while the Bernstein polynomials are normalized Gibbs traces.
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BibTeX
@misc{silva2026finite,
title = {{Finite Rodriguez-Villegas Approximants to the Riemann $ξ$-Function}},
author = {Alisson M. Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25564},
eprint = {2609.25564},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25564},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite Rodriguez-Villegas Approximants to the Riemann ξ-Function
AU - Alisson M. Silva
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25564
UR - https://arxiv.org/abs/2609.25564
AB - We construct a sequence of finite Rodriguez-Villegas transforms converging locally uniformly to the Riemann ξ-function in the critical strip. The input is a positive symmetric profile on the unit interval obtained from the Riemann theta kernel through convolution with the hyperbolic-secant kernel and the logistic coordinate. The profile is a Stieltjes function of x(1−x). Its Bernstein polynomials produce reciprocal numerators and exact finite functional equations. The same numerators admit an exact realization as fermionic supertraces, while the Bernstein polynomials are normalized Gibbs traces.
ER -