Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
Connes, Alain
Journées équations aux dérivées partielles, (1997), p. 1-28 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@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},
     year = {1997},
     pages = {1-28},
     zbl = {01808664},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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), pp. 1-28. http://gdmltest.u-ga.fr/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 35 #3701 | Zbl 0161.43201

[B] M. Berry, Riemann's zeta function: a model of quantum chaos, Lecture Notes in Physics, 263, Springer (1986). | Zbl 0664.10021

[Bg] A. Beurling, A closure problem related to the Riemann zeta function, Proc. Nat. Ac. Sci. 41 (1955), 312-314. | MR 17,15a | Zbl 0065.30303

[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 96m:46112 | Zbl 0842.46040

[BG] O. Bohigas and M. Giannoni, Chaotic motion and random matrix theories, Lecture Notes in Physics, 209 (1984), 1-99. | MR 86c:58129

[C] A. Connes, Noncommutative Geometry, Academic Press (1994). | MR 95j:46063 | Zbl 0818.46076

[Co] A. Connes, Formule de trace en Géométrie non commutative et hypothèse de Riemann, C.R. Acad. Sci. Paris Ser. A-B (1996). | MR 97k:11124 | Zbl 0864.46042

[D] C. Deninger, Local L-factors of motives and regularised determinants, Invent. Math., 107 (1992), 135-150. | MR 93a:11056 | Zbl 0762.14015

[G] D. Goldfeld, A spectral interpretation of Weil's explicit formula, Lecture Notes in Math., 1593, Springer Verlag (1994), 135-152. | MR 96f:11110 | Zbl 0828.11031

[GS] V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, 14, Amer. Math. Soc., Providence, R.I. (1977). | MR 58 #24404 | Zbl 0364.53011

[Gu] V. Guillemin, Lectures on spectral theory of elliptic operators, Duke Math. J., 44, No.3 (1977), 485-517. | MR 56 #6758 | Zbl 0447.58033

[H] S. Haran, Riesz potentials and explicit sums in arithmetic, Invent. Math., 101 (1990), 697-703. | MR 91g:11132 | Zbl 0788.11055

[J] B. Julia, Statistical theory of numbers, Number Theory and Physics, Springer Proceedings in Physics, 47 (1990). | MR 91h:11088 | Zbl 0727.11033

[K] M. Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Math. Monographs 18 (1959). | Zbl 0088.10303

[KS] N. Katz and P. Sarnak, Random matrices, Frobenius eigenvalues and Monodromy, (1996), Book, to appear. | Zbl 0958.11004

[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 49 #2590 | Zbl 0268.10023

[O] A. Odlyzko, On the distribution of spacings between zeros of zeta functions, Math. Comp. 48 (1987), 273-308. | MR 88d:11082 | Zbl 0615.10049

[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 89d:11072 | Zbl 0641.10029

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

[W1] A. Weil, Basic Number Theory, Springer, New York (1974). | MR 55 #302 | Zbl 0326.12001

[W2] A. Weil, Fonctions zêta et distributions, Séminaire Bourbaki, 312, (1966). | Numdam | Zbl 0226.12008

[W3] A. Weil, Sur les formules explicites de la théorie des nombres, Izv. Mat. Nauk., (Ser. Mat.) 36, 3-18. | MR 52 #345 | Zbl 0245.12010

[Z] D. Zagier, Eisenstein series and the Riemannian zeta function, Automorphic Forms, Representation Theory and Arithmetic, Tata, Bombay (1979), 275-301. | MR 83j:10027 | Zbl 0484.10019