most citedFrom Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory

58 citations · 166 across the 6 of their papers we have counts for

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math.OA2005★ 7 cited

KMS states and complex multiplication

Alain Connes, Matilde Marcolli, Niranjan Ramachandran

We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the e…

math.OA2003★ 18 cited

L^2-Homology for von Neumann Algebras

Alain Connes, Dimitri Shlyakhtenko

We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these i…