On a noncommutative reciprocity law

Details On a noncommutative reciprocity law On a noncommutative reciprocity law

2009-12-24

arxiv.org/abs/0912.4905v3

Mathematics

Operator Algebras

12 pages; revised

Scientific paper

We prove a reciprocity relation, which says that an L-function of the noncommutative torus with real multiplication coincides with the Hasse-Weil L-function of an elliptic curve with complex multiplication. Our proof is based on an explicit formula for the Teichmueller functor between elliptic curves and noncommutative tori. The result entails, that the Cuntz-Krieger algebras are isomorphic to elliptic curves over finite fields.

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