Parity of $k$-differentials in genus zero and one

Summary · qwen2.5:32b

The article determines the spin parity of $k$-differentials with specified zero and pole orders on Riemann surfaces of genus zero and one, confirming a previously conjectured result. This achievement resolves Conjecture A.10 by reformulating it using Jacobi symbols, and the proof was formalized in Lean/Mathlib by AxiomProver.

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An exciting new result on the parity of k-differentials in genus zero and one has been determined, shedding light on a conjecture in number theory. This work was proven using AxiomProver and Lean/Mathlib.

Excerpt

arXiv:2602.03722v2 Announce Type: replace Abstract: Here we completely determine the spin parity of $k$-differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtained conditionally by the first author and Quentin Gendron assuming the truth of a number-theoretic hypothesis Conjecture A.10. We prove this hypothesis by reformulating it in terms of Jacobi symbols, reducing the proof to a combinatorial identity and standard facts about Jacobi symbols. The proof was obtained by AxiomProver and the system formalized the proof of the combinatorial identity in Lean/Mathlib (see the Appendix).