A Universal Leading-Residue Formula for Witten Zeta Functions
For an irreducible crystallographic root system of rank with Coxeter number , the paper proves that Au's normalized Witten zeta function has a simple pole at and evaluates its residue in closed form in terms of the Cartan determinant, the Weyl group order and the invariant degrees.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Zeta Functions, Root Systems
- Posed by
- Arising from Au's work on Witten zeta functions
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-14
- Model
- GPT-5.6 Sol via Codex
- Vendor
- OpenAI
- Collaborators
- Jonas Matuzas
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The most complete authorship claim in this batch: the paper states that all mathematical derivations, proofs, exposition, computational code and publication materials were generated and written entirely in Codex using GPT-5.6 Sol, with Codex Ultra mode for multi-agent work, and that GPT-5.6 Pro was used separately in the ChatGPT web app to review the derivations.
Verification
No independent review, and the author describes the entire mathematical content as machine-generated, reviewed by a second model rather than by a person. Treat accordingly. Preprint, not refereed.