PreprintCC BY-NC-ND 4.0HAL
Computational verification of the Riemann hypothesis via differential equations
Abstract
Although the numerical search for non-trivial zeros of the Riemann zeta function is important, this short paper presents a computational method based on linear differential equations to detect regions in the critical strip where the symmetry of the zeta function breaks down. Rather than directly searching for non-trivial zeros, the proposed approach provides a computational procedure for excluding regions in the critical strip where such zeros cannot occur.
Related
- Existence and multiplicity results for third-order ordinary differential equations with derivative dependence subject to the Riemann–Stieltjes integral boundary conditions
- Currently, there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
- A Formal Proof of Riemann Hypothesis from Existence Alone, the Sign Excepted by Theorem: The Constructed Witness, the Identity Cone over the Fixed Locus, the Grounded Counter-Model, and the Cure Theorem Proved in Lean 4 and Re-executed in Fortran
- Ramanujan Conjecture and Riemann Hypothesis for the unitary groups over function fields
- Proof of the Riemann Hypothesis through the limit of an approximated ξ function
BibTeX
@misc{oukil2026computational,
title = {{Computational verification of the Riemann hypothesis via differential equations}},
author = {W Oukil},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-03581978v44},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Computational verification of the Riemann hypothesis via differential equations
AU - W Oukil
PY - 2026
DA - 2026/09/30
PB - HAL
UR - https://hal.science/hal-03581978v44
AB - Although the numerical search for non-trivial zeros of the Riemann zeta function is important, this short paper presents a computational method based on linear differential equations to detect regions in the critical strip where the symmetry of the zeta function breaks down. Rather than directly searching for non-trivial zeros, the proposed approach provides a computational procedure for excluding regions in the critical strip where such zeros cannot occur.
ER -