The spherical Hall algebra of Spec(O_K) for class-number-one K is isomorphic to the Paley-Wiener shuffle algebra of the Hecke L-function L_K.
Onishchik and Ernest B
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The spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$
The spherical Hall algebra of Spec(O_K) for class-number-one K is isomorphic to the Paley-Wiener shuffle algebra of the Hecke L-function L_K.