The paper constructs J-self-adjoint causal operator pencils whose spectral determinants encode the local Euler factors of L-functions, proving a universal matching theorem for elliptic curves when the spectral curve has genus 1.
Compositio Math
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A Local Hilbert--P\'olya Realisation for Elliptic Curve $L$-Functions
The paper constructs J-self-adjoint causal operator pencils whose spectral determinants encode the local Euler factors of L-functions, proving a universal matching theorem for elliptic curves when the spectral curve has genus 1.