A C * -dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking
Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 15-30.

Dans cet article nous étendons une construction de Bost-Connes, au cas d’un corps de nombres quelconque, d’un C * -système dynamique à brisure spontanée de symétrie et fonction de partition la fonction zêta de Riemann.

In this paper we extend to arbitrary number fields a construction of Bost-Connes of a C * -dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.

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     title = {A $C^\ast $-dynamical system with {Dedekind} zeta partition function and spontaneous symmetry breaking},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {15--30},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {1},
     year = {1999},
     mrnumber = {1730430},
     zbl = {0962.11031},
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Cohen, Paula B. A $C^\ast $-dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 15-30. http://archive.numdam.org/item/JTNB_1999__11_1_15_0/

[ALR] J. Arledge, M. Laca and I. Raeburn, Semigroup crossed products and Hecke algebras arising from number fields, Doc. Mathematica 2 (1997) 115-138. | MR | Zbl

[BC] J-B. Bost and A. Connes, Hecke algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theory, Selecta Math. (New Series), 1 (1995), 411-457. | MR | Zbl

[C] A. Connes, Formule de trace en géométrie non commutative et hypothèse de Riemann, C. R. Acad. Sci. Paris t.323, Série 1 (Analyse), (1996) 1231-1236. | MR | Zbl

[HaLe] D. Harari and E. Leichtnam, Extension du phénomène de brisure spontanée de symétrie de Bost-Connes au cas des corps globaux quelconques, Selecta Mathematica, New Series 3 (1997), 205-243. | MR | Zbl

[J] B. Julia, Statistical Theory of Numbers, in Number Theory and Physics, Les Houches Winter School, J-M. Luck, P. Moussa, M. Waldschmidt eds., Springer Proceedings in Physics 47 (1990), 276-293. | MR | Zbl

[L] M. Laca, Semigroups of * -endomorphisms, Dirichlet series and Phase Transitions, J. Functional Analysis, to appear. | MR | Zbl

[LR1] M. Laca and I. Raeburn, Semigroup crossed products and the Toeplitz algebras of non-abelian groups, J. Functional Analysis 139 (1996), 415-440. | MR | Zbl

[LR2] M. Laca and I. Raeburn, A semigroup crossed product arising in number theory, J. London Math. Soc., to appear. | MR | Zbl

[Lg] S. Lang, Algebraic Number Theory, Second Edition, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1994. | MR | Zbl

[N] J. Neukirch, Class Field Theory, Grund. der math. Wissen. 280, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1980. | MR | Zbl

[Ni] A. Nica, C* - algebras generated by isometries and Wiener-Hopf operators, J. Operator Theory 27 (1992), 17-52. | MR | Zbl