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Modular forms and root systems

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References

  1. Bourbaki, N.: Groupes et algèbres de Lie, Chap. IV, V, VI. Paris: Hermann 1968

    Google Scholar 

  2. Chevalley, C.: Invariants of finite groups generated by reflections. Amer. J. Math.77, 778–782 (1955)

    Google Scholar 

  3. Flatto, L.: Invariants of finite reflection groups and mean value problems II. Amer. J. Math.92, 552–561 (1970)

    Google Scholar 

  4. Frame, J. S.: The classes and representations of the groups of 27 lines and 28 bitangents. Ann. Mat. Pura Appl. (4),32, 83–119 (1951)

    Google Scholar 

  5. Freudenthal, H., de Vries, H.: Linear Lie groups. London, New York: Academic Press 1969

    Google Scholar 

  6. Gunning, R. C.: Lectures on modular forms, Annals of Mathematics Studies 48. New York: Princeton University Press 1962

    Google Scholar 

  7. MacDonald, I. G.: Affine root systems and Dedekind's η-function. Inv. Math.15, 91–143 (1972)

    Google Scholar 

  8. Ogg, A.: Modular forms and Dirichlet series. New York: Benjamin 1969

    Google Scholar 

  9. Pfetzer, W.: Die Wirkung der Modulsubstitutionen auf mehrfache Thetareihen zu quadratischen Formen ungerader Variablenzahl. Arch. Math.IV, 448–454 (1953)

    Google Scholar 

  10. Schoeneberg, B.: Das Verhalten von mehrfachen Thetareihen bei Modulsubstitutionen. Math. Ann.116, 511–523 (1939)

    Google Scholar 

  11. Siegel, C. L.: A simple proof of\(\eta \left( { - \frac{1}{\tau }} \right) = \eta \left( \tau \right)\sqrt {\frac{\tau }{i}} \). Mathematika1, 4 (1954)

    Google Scholar 

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van Asch, A.G. Modular forms and root systems. Math. Ann. 222, 145–170 (1976). https://doi.org/10.1007/BF01418325

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