Paula B. Cohen
Dedekind Zeta Functions and Quantum Statistical Mechanics
Preprint series: ESI preprints
11M26 Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
11R42 Zeta functions and $L$-functions of number fields, See also {11M41, 19F27}
11S40 Zeta functions and $L$-functions, See also {11M41, 19F27}
46L55 Noncommutative dynamical systems, See also {28Dxx, 54H20,
Abstract: In this article we construct a C*-dynamical system with partition function the Dedekind zeta function of a given number field and with a phase transition at the pole of this zeta function which detects a breaking of symmetry with respect to a natural symmetry group. This extends work of Bost-Connes and Harari-Leichtnam.

Keywords: C*-Hecke Algebras, zeta functions, C*-dynamical systems


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