The paper proves (up to an explicit Legendre symbol) that the Frobenius trace on the theta line bundle over the Jacobian equals an arithmetic path integral over ℓ-torsion points, but the trace formula relies on a false multiplicativity lemma.
On Uniformity Conjectures for Abelian Varieties and K3 Surfaces
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A Trace-Path Integral Formula over Function Fields
The paper proves (up to an explicit Legendre symbol) that the Frobenius trace on the theta line bundle over the Jacobian equals an arithmetic path integral over ℓ-torsion points, but the trace formula relies on a false multiplicativity lemma.