@incollection{JEDP_1997____A4_0, author = {Connes, Alain}, title = {Trace formula in noncommutative {Geometry} and the zeros of the {Riemann} zeta function}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {4}, pages = {1--28}, publisher = {Ecole polytechnique}, year = {1997}, zbl = {01808664}, language = {en}, url = {http://archive.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://archive.numdam.org/item/JEDP_1997____A4_0/ LA - en ID - JEDP_1997____A4_0 ER -
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://archive.numdam.org/item/JEDP_1997____A4_0/
[AB] A Lefchetz fixed point formula for elliptic complexes: I, Annals of Math, 86 (1967), 374-407. | MR | Zbl
and ,[B] Riemann's zeta function: a model of quantum chaos, Lecture Notes in Physics, 263, Springer (1986). | Zbl
,[Bg] A closure problem related to the Riemann zeta function, Proc. Nat. Ac. Sci. 41 (1955), 312-314. | MR | Zbl
,[B-C] 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
and ,[BG] Chaotic motion and random matrix theories, Lecture Notes in Physics, 209 (1984), 1-99. | MR
and ,[C] Noncommutative Geometry, Academic Press (1994). | MR | Zbl
,[Co] Formule de trace en Géométrie non commutative et hypothèse de Riemann, C.R. Acad. Sci. Paris Ser. A-B (1996). | MR | Zbl
,[D] Local L-factors of motives and regularised determinants, Invent. Math., 107 (1992), 135-150. | EuDML | MR | Zbl
,[G] A spectral interpretation of Weil's explicit formula, Lecture Notes in Math., 1593, Springer Verlag (1994), 135-152. | MR | Zbl
,[GS] Geometric asymptotics, Math. Surveys, 14, Amer. Math. Soc., Providence, R.I. (1977). | MR | Zbl
and ,[Gu] Lectures on spectral theory of elliptic operators, Duke Math. J., 44, No.3 (1977), 485-517. | MR | Zbl
,[H] Riesz potentials and explicit sums in arithmetic, Invent. Math., 101 (1990), 697-703. | MR | Zbl
,[J] Statistical theory of numbers, Number Theory and Physics, Springer Proceedings in Physics, 47 (1990). | MR | Zbl
,[K] Statistical Independence in Probability, Analysis and Number Theory, Carus Math. Monographs 18 (1959). | Zbl
,[KS] Random matrices, Frobenius eigenvalues and Monodromy, (1996), Book, to appear. | Zbl
and ,[KS] Zeros of zeta functions, their spacings and spectral nature, (1997), to appear.
and ,[M] The pair correlation of zeros of the zeta function, Analytic Number Theory, AMS (1973). | MR | Zbl
,[O] On the distribution of spacings between zeros of zeta functions, Math. Comp. 48 (1987), 273-308. | MR | Zbl
,[P] Collected Papers, Cambridge, M.I.T. Press (1974).
,[Pat] An introduction to the theory of the Riemann zeta function, Cambridge Studies in advanced mathematics, 14 Cambridge University Press (1988). | MR | Zbl
,[R] Mathematical Werke, Dover, New York (1953).
,[W1] Basic Number Theory, Springer, New York (1974). | MR | Zbl
,[W2] Fonctions zêta et distributions, Séminaire Bourbaki, 312, (1966). | Numdam | Zbl
,[W3] Sur les formules explicites de la théorie des nombres, Izv. Mat. Nauk., (Ser. Mat.) 36, 3-18. | MR | Zbl
,[Z] Eisenstein series and the Riemannian zeta function, Automorphic Forms, Representation Theory and Arithmetic, Tata, Bombay (1979), 275-301. | MR | Zbl
,