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On a Certain Function Analogous to log|η(z)|

Published online by Cambridge University Press:  22 January 2016

Tetsuya Asai
Tetsuya Asai*
Affiliation:
Mathematical Institute, Nagoya University
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The purpose of this paper is to give the limit formula of the Kronecker’s type for a non-holomorphic Eisenstein series with respect to a Hubert modular group in the case of an arbitrary algebraic number field. Actually, we shall generalize the following result which is well-known as the first Kronecker’s limit formula. From our view-point, this classical case is corresponding to the case of the rational number field Q.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 193 - 211
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Hecke, E., Über die Konstruktion der Klassenkörper reeller quadratischer Körper mit Hilfe von automorphen Funktionen, Math. Werke, 64–68.Google Scholar
[2] Hecke, E., Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen, Math. Werke, 215–234.Google Scholar
[3] Hecke, E., Analytische Funktionen und algebraische Zahlen, I, II, Math. Werke, 336–360, 381–404.Google Scholar
[4] Herrmann, O., Öber Hilbertsche Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung, Math. Ann. 127, 357–400, (1954).CrossRefGoogle Scholar
[5] Katayama, K., Kronecker’s limit formulas and their applications, J. Fac. Sci., Univ. of Tokyo, Sect. I, 13, 1–44, (1966).Google Scholar
[6] 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, 411–424, (1965).CrossRefGoogle Scholar
[7] Kubota, T., Über diskontinuierlicher Gruppen Picardschen Typus und zugehorige Eisensteinsche Reihen, Nagoya Math. J. 32, 259–271, (1968).CrossRefGoogle Scholar
[8] Kubota, T., On automorphic functions and the reciprocity law in a number field, Lectures in Math. 2, Kyoto Univ. (1969).Google Scholar
[9] Maass, H., Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121, 141–183, (1949).CrossRefGoogle Scholar
[10] Magnus, Oberhettinger and Soni, , Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. Springer-Verlag, 1966.CrossRefGoogle Scholar
[11] Siegel, C.L., Analytische Zahlentheorie II, Vorlesung an der Univ. Göttingen, 1963/64.Google Scholar
[12] Tamagawa, T., On some extensions of Epstein’s Z-series, Proc. International Symposium on algebraic number theory, Tokyo-Nikko, 1955, 259–261.Google Scholar
[13] Weil, A., Sur une formule classique, J. Math. Soc. Japan, 20, 400–402, (1968).Google Scholar