Article PDF
Avoid common mistakes on your manuscript.
References
Atiyah, M.F.: The signature of fibre-bundles. Global Analysis, 73–84. Tokyo, Princeton: University Press 1969
Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes. II. Ann. Math.88, 451–491 (1968)
Atiyah, M.F., Singer, I.M.: The index of elliptic operators. I, III. Ann. Math.87, 484–530, 546–604 (1968)
Atiyah, M.F., Singer, I.M.: The index of elliptic operators. IV. Ann. Math.93, 119–138 (1971)
Atiyah, M.F., Donnelly, H., Singer, I.M.: Eta invariants, signature defects of cusps and values of L-functions. Ann. Math.118, 131–177 (1983)
Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. I. Math. Proc. Camb. Phil. Soc.77, 43–69 (1975)
Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. II. Math. Proc. Camb. Phil. Soc.78, 405–432 (1975)
Bismut, J.M.: The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs. Invent. Math.83, 91–151 (1986)
Bismut, J.M., Freed, D.S.: The analysis of elliptic families, I. Metrics and connections on determinant bundles. Commun. Math. Phys.106, 159–176 (1986)
Bismut, J.M., Freed, D.S.: The analysis of elliptic families. II. Commun. Math. Phys.107, 103–163 (1986)
Chern, S.S., Hirzebruch, F., Serre, J.-P.: The index of a fibered manifold. Proc. Am. Math. Soc.8, 587–596 (1957)
Dedekind, R.: Erläuterungen zu zwei Fragmenten von Riemann. Riemann's gesammelte Mathematische Werke 2, 466–478. New York: Dover 1982
Deligne, P.: Equations différentielles à points singulier réguliers. Lect. Notes Math. 163. Berlin, Heidelberg, New York: Springer 1970
Donnelly, H., Patodi, V.K.: Spectrum and the fixed point sets of isometries II. Topology16, 1–12 (1977)
Freed, D.S. (to appear)
Donaldson, S.K.: Infinite determinants, stable bundles and curvatur. Duke. Math. J.54, 231–247 (1987)
Hirzebruch, F.: Hilbert modular surfaces. Enseign. Math.19, 183–281 (1973)
Hirzebruch, F.: The signature theorem: reminiscences and recreation. Prospects in Mathematics. Ann. Math. Stud.70, pp. 3–31. Princeton, University Press 1971
Hochschild, G.: Group extensions of Lie groups. II. Ann. Math.54, 537–551 (1951)
Kodaira, K.: A certain type of irregular algebraic surfaces. J. Analyse Math.19, 207–215 (1967)
Kodaira, K.: On compact analytic surfaces. Analytic Functions, 121–136 Princeton: Univ. Press (1960)
Lusztig, G.: Novikov's higher signature theorem and families of elliptic operators. J. Differ. Geometry7, 229–256 (1972)
Mackey, G.W.: Les ensembles Borélien et les extensions des groupes. J. Math. Pures. Appl.36, 171–178 (1957)
Meyer, C.: Über die Bildung von Klasseninvarianten. Abh. Math. Sem. Univ. Hamburg27, 206–230 (1964)
Meyer, C.: Die Berechnung der Klassenzahl abelscher Körper über quadratischen Zahlenkörpern. Berlin 1957
Meyer, W.: Die Signatur von Flächenbündeln. Math. Ann.201, 239–264 (1973)
Meyer, W., Sczech, R.: Über eine topologische und Zahlentheoretische Anwendung von Hirzebruchs Spitzenauflösung. Math. Ann.240, 69–96 (1979)
Müller, W.: Signature defects of cusps of Hilbert modular varieties and values of L-functions at s=1. Akademie der Wissenschaften der DDR, preprint 1983
Mumford, D.: Abelian quotients of the Teichmüller modular group. J. d'Analyse Math.18, 227–244 (1967)
Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. Funct. Anal. Appl.19, 31–34 (1985)
Quillen, D.: Superconnections and the Chern character. Topology24, 89–95 (1985)
Rademacher, K.: Zur Theorie der Dedekindschen Summen. Math. Zeit63, 445–463 (1956)
Ray, D.B., Singer, I.M.: R-torsion and the Laplacian on Riemannian manifolds. Adv. Math.7, 145–210 (1971)
Ray, D.B., Singer, I.M.: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)
Siegel, C.L.: Advanced Analytic Number Theory. Tata Institute of Fundamental Research, Bombay 1980
Witten, E.: Global gravitational anomalies. Commun. Math. Phys.100, 197–229 (1985)
Author information
Authors and Affiliations
Additional information
Dedicated to Friedrich Hirzebruch
Rights and permissions
About this article
Cite this article
Atiyah, M. The logarithm of the dedekind η-function. Math. Ann. 278, 335–380 (1987). https://doi.org/10.1007/BF01458075
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01458075