Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
Journées équations aux dérivées partielles (1997), article no. 4, 28 p. 
@article{JEDP_1997____A4_0,
     author = {Connes, Alain},
     title = {Trace formula in noncommutative {Geometry} and the zeros of the {Riemann} zeta function},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {4},
     pages = {1--28},
     publisher = {Ecole polytechnique},
     year = {1997},
     zbl = {01808664},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1997____A4_0/}
}
TY  - JOUR
AU  - Connes, Alain
TI  - Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
JO  - Journées équations aux dérivées partielles
PY  - 1997
SP  - 1
EP  - 28
PB  - Ecole polytechnique
UR  - http://www.numdam.org/item/JEDP_1997____A4_0/
LA  - en
ID  - JEDP_1997____A4_0
ER  - 
%0 Journal Article
%A Connes, Alain
%T Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
%J Journées équations aux dérivées partielles
%D 1997
%P 1-28
%I Ecole polytechnique
%U http://www.numdam.org/item/JEDP_1997____A4_0/
%G en
%F JEDP_1997____A4_0
Connes, Alain. Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function. Journées équations aux dérivées partielles (1997), article  no. 4, 28 p. http://www.numdam.org/item/JEDP_1997____A4_0/

[AB] M.F. Atiyah and R. Bott, A Lefchetz fixed point formula for elliptic complexes: I, Annals of Math, 86 (1967), 374-407. | MR | Zbl

[B] M. Berry, Riemann's zeta function: a model of quantum chaos, Lecture Notes in Physics, 263, Springer (1986). | Zbl

[Bg] A. Beurling, A closure problem related to the Riemann zeta function, Proc. Nat. Ac. Sci. 41 (1955), 312-314. | MR | Zbl

[B-C] J.-B. Bost and A. Connes, Hecke Algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theory, Selecta Mathematica, New Series 1, No. 3 (1995), 411-457. | MR | Zbl

[BG] O. Bohigas and M. Giannoni, Chaotic motion and random matrix theories, Lecture Notes in Physics, 209 (1984), 1-99. | MR

[C] A. Connes, Noncommutative Geometry, Academic Press (1994). | MR | Zbl

[Co] A. Connes, Formule de trace en Géométrie non commutative et hypothèse de Riemann, C.R. Acad. Sci. Paris Ser. A-B (1996). | MR | Zbl

[D] C. Deninger, Local L-factors of motives and regularised determinants, Invent. Math., 107 (1992), 135-150. | EuDML | MR | Zbl

[G] D. Goldfeld, A spectral interpretation of Weil's explicit formula, Lecture Notes in Math., 1593, Springer Verlag (1994), 135-152. | MR | Zbl

[GS] V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, 14, Amer. Math. Soc., Providence, R.I. (1977). | MR | Zbl

[Gu] V. Guillemin, Lectures on spectral theory of elliptic operators, Duke Math. J., 44, No.3 (1977), 485-517. | MR | Zbl

[H] S. Haran, Riesz potentials and explicit sums in arithmetic, Invent. Math., 101 (1990), 697-703. | MR | Zbl

[J] B. Julia, Statistical theory of numbers, Number Theory and Physics, Springer Proceedings in Physics, 47 (1990). | MR | Zbl

[K] M. Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Math. Monographs 18 (1959). | Zbl

[KS] N. Katz and P. Sarnak, Random matrices, Frobenius eigenvalues and Monodromy, (1996), Book, to appear. | Zbl

[KS] N. Katz and P. Sarnak, Zeros of zeta functions, their spacings and spectral nature, (1997), to appear.

[M] H. Montgomery, The pair correlation of zeros of the zeta function, Analytic Number Theory, AMS (1973). | MR | Zbl

[O] A. Odlyzko, On the distribution of spacings between zeros of zeta functions, Math. Comp. 48 (1987), 273-308. | MR | Zbl

[P] G. Pólya, Collected Papers, Cambridge, M.I.T. Press (1974).

[Pat] S. Patterson, An introduction to the theory of the Riemann zeta function, Cambridge Studies in advanced mathematics, 14 Cambridge University Press (1988). | MR | Zbl

[R] B. Riemann, Mathematical Werke, Dover, New York (1953).

[W1] A. Weil, Basic Number Theory, Springer, New York (1974). | MR | Zbl

[W2] A. Weil, Fonctions zêta et distributions, Séminaire Bourbaki, 312, (1966). | Numdam | Zbl

[W3] A. Weil, Sur les formules explicites de la théorie des nombres, Izv. Mat. Nauk., (Ser. Mat.) 36, 3-18. | MR | Zbl

[Z] D. Zagier, Eisenstein series and the Riemannian zeta function, Automorphic Forms, Representation Theory and Arithmetic, Tata, Bombay (1979), 275-301. | MR | Zbl