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A Note on Hecke Operators and Theta-Series

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Mathematical Institute, Nagoya University.
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As typical examples of modular forms there are theta series and Eisenstein series. We can easily see the behaviour of the Hecke operator on the Eisenstein series but it is very difficult to know that on the theta series.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 189 - 195
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Hecke, E., Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I, II, Math. Ann. 114 (1937), 1–28, 316–351.Google Scholar
[2] Maass, H., Konstruktion genzer Modulformen halbzahliger Dimension mit ϑ-Multiplikatoren in einer und zwei Variablen, Abh. Math. Sem. Hamburg, 12 (1938), 133–162.Google Scholar
[3] Schoeneberg, B., Das Verhalten von mehrfachen Thetareihen bei Modulsubstitutionen, Math. Ann. 116 (1939), 511–523.Google Scholar
[4] Siegel, C.L., Über die analytische Theorie der quadratischen Foremen, Ann. of Math. 36 (1935), 527–606.Google Scholar