# On the arithmetic of the BC-system

@article{Connes2011OnTA,
title={On the arithmetic of the BC-system},
author={Alain Connes and Caterina Consani},
journal={arXiv: Quantum Algebra},
year={2011}
}
• Published 24 March 2011
• Mathematics
• arXiv: Quantum Algebra
For each prime p and each embedding of the multiplicative group of an algebraic closure of F_p as complex roots of unity, we construct a p-adic indecomposable representation of the integral BC-system as additive endomorphisms of the big Witt ring of an algebraic closure of F_p. The obtained representations are the p-adic analogues of the complex, extremal KMS states at zero temperature of the BC-system. The role of the Riemann zeta function, as partition function of the BC-system over complex…

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