Skip to main content
Log in

Theta series on the Hecke groupsG(\(\sqrt 2 \)) andG (\(\sqrt 3 \))

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Eichler, M.: The basis problem for modular forms and the traces of the Hecke operators. Lecture Notes in Math.320, 75–151 (1973). Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  2. Hecke, E.: Mathematische Werke 3. Aufl. Göttingen: Vandenhoeck u. Ruprecht 1983

    Google Scholar 

  3. Hutchinson, J.I.: On a class of automorphic functions. Trans. Am. Math. Soc.3, 1–11 (1902)

    Google Scholar 

  4. Kern-Isberner, G., Rosenberger, G.: A note on numbers of the formn=x 2+N y2. Arch. Math.43, 148–156 (1984)

    Google Scholar 

  5. Klein, F., Fricke, R.: Vorlesungen über die Theorie der elliptischen Modulfunktionen, Band 2. Leipzig: Teubner 1892

    Google Scholar 

  6. Knopp, M.: Determination of certain roots of unity in the theory of automorphic forms of dimension zero. Duke Math. J.27, 497–506 (1960)

    Google Scholar 

  7. Köhler, G.: Observations on Hecke eigenforms on the Hecke groupsG(\(\sqrt 2 \)) andG (\(\sqrt 3 \)). Abh. Math. Seminar Univ. Hamburg55, 75–89 (1985)

    Google Scholar 

  8. Leutbecher, A.: Über die Heckeschen GruppenG(λ). Abh. Math. Seminar Univ. Hamburg31, 199–205 (1967). Teil II: Math. Ann.211, 63–86 (1974)

    Google Scholar 

  9. Lint, J.H. van: Hecke operators and Euler products. Thesis, Utrecht 1957

  10. Maaß, H.: Lectures on modular functions of one complex variable 2nd ed. Berlin-Heidelberg-New York: Springer 1983

    Google Scholar 

  11. Mordell, L.J.: On Mr Ramanujan's empirical expansions of modular functions. Proc. Cambridge Phil. Soc.19, 117–124 (1917)

    Google Scholar 

  12. Newman, M.: A table of coefficients of the powers of η(τ). Indagationes Math.18, 204–216 (1956)

    Google Scholar 

  13. Petersson, H.: Über einen einfachen Typus von Untergruppen der Modulgruppe. Arch. Math.4, 308–315 (1953)

    Google Scholar 

  14. Petersson, H.: Über gewisse Dirichlet-Reihen mit Eulerscher Produktzerlegung. Math. Z.189, 273–288 (1985)

    Google Scholar 

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

    Google Scholar 

  16. Schoeneberg, B.: Über den Zusammenhang der Eisensteinschen Reihen und Thetareihen mit der Diskriminante der elliptischen Funktionen. Math. Ann.126, 177–184 (1953)

    Google Scholar 

  17. Serre, J.P.: Sur la lacunarité des puissances de η. Glasgow Math. J.27, 203–221 (1985)

    Google Scholar 

  18. Shimura, G.: On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields. Nagoya Math. J.43, 199–208 (1971)

    Google Scholar 

  19. Smart, J.R.: Parametrization of the automorphic forms for the Hecke groupsG(\(\sqrt 2 \)) andG (\(\sqrt 3 \)). Duke Math. J.31, 395–404 (1964)

    Google Scholar 

  20. Gauss, C.F.: Werke, 8. Band. Hrsg. Kgl. Ges. d. Wiss. Göttingen. Leipzig: B.G. Teubner 1900

    Google Scholar 

  21. Köhler, G.: Theta series on the theta group. Abh. Math. Seminar Univ. Hamburg58 (1988)

  22. Satgé, P.: Décomposition des nombres premiers dans des extensions non abéliennes. Ann. de l'Inst. Fourier27, 1–8 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Köhler, G. Theta series on the Hecke groupsG(\(\sqrt 2 \)) andG (\(\sqrt 3 \)). Math Z 197, 69–96 (1988). https://doi.org/10.1007/BF01161631

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01161631

Keywords

Navigation