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On the analytic function which appears in Kronecker’s limit formula for CM-fields

Published online by Cambridge University Press:  22 January 2016

Toshiaki Suzuki
Toshiaki Suzuki*
Affiliation:
Department of Mathematics, Ryukyu University, Okinawa, Japan
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Hecke stated in [1] Kronecker’s limit formula for CM-fields without proof, in which “Die zu log η(z) analog Funktion” appears, and he investigated in [3] the behaviors of this function under modular substitutions. S. Konno also discussed Kronecker’s limit formula for CM-fields in [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 103 , October 1986 , pp. 1 - 13
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[1] Hecke, E., Über die Konstruktion der Klassenkörper reeller quadratischer Körper mit Hilfe von automorphen Funktionen, Math. Werke, Göttingen • Vandenhoeck & Ruprecht, 1959, 64–68.Google Scholar
[2] Hecke, E., Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen, Math. Werke, Gottingen’Vandenhoeck & Ruprecht, 1959, 215–234.Google Scholar
[3] Hecke, E., Analytische Funktionen und algebraische Zahlen, I, II, Math. Werke Göttingen. Vandenhoeck & Ruprecht, 1959, 336–360, 381–404.Google Scholar
[4] Konno, S., On Kronecker’s limit formula in a totally imaginary quadratic field over a totally real algebraic number field, J. Math. Soc. Japan, 17 (1965), 411–424.Google Scholar
[5] Siegel, C. L., Uber die Fourierschen Koeffizienten von Modulformen, Göttingen Nachr. Akad. Wiss., 1970, 15–56.Google Scholar
[6] Weil, A., Elliptic functions according to Eisenstein and Kronecker, Sprirger-Verlag-Berlin-Heidelberg-New York (1976).Google Scholar