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The theory of Hecke integrals

Published online by Cambridge University Press:  22 January 2016

Larry Joel Goldstein  and
Michael Razar
Larry Joel Goldstein
Affiliation:
University of Maryland
Michael Razar
Affiliation:
University of Maryland
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Let H denote the complex upper half-plane and let η(z) denote Dedekind’s η-function

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 63 , October 1976 , pp. 93 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Borevich, Z. I. and Shafarevich, I. Number Theory, Academic Press, New York, 1966.Google Scholar
[2] Davenport, H. Multiplicative Number Theory, Markham Publ. Co., Chicago, 1967.Google Scholar
[3] Dedekind, R. “Erlauterungen zu Zwei Fragmenten von Riemanns,” Gess. Math. Werke, vol. 1 (1930), pp. 159–173.Google Scholar
[4] Goldstein, L. and de la Torré, P. “On the transformation of log η(r) ,” Duke Math. J. (1973), pp. 291–297.Google Scholar
[5] Hecke, E. “Über die Bestimmung Dirichletscher Reihen durch ihre Funktional-gleichung,” Math. Ann. 112 (1936), pp. 664–699.Google Scholar
[6] Hecke, E. “Bestimmung der Klassenzahl einer neuen Riehe von algebraischen Zahlkörpern,” Math. Werke, p. 290–312.Google Scholar
[7] Meyer, C. Die Berechnung der Klassenzahl Abelscher Körper über quadratischen Zahlkörpern, Berlin: Akademie-Verlag, 1957.Google Scholar
[8] Ogg, A. Dirichlet Series and Modular Forms, Benjamin, New York, 1966.Google Scholar
[9] Rademacher, H. “On the transformation of log η(z),” J. Indian Math. Soc. 19 (1955), pp. 25–30.Google Scholar
[10] Rademacher, H. “Zur Theorie der Modulfunktionen,” Crelle 167 (1931), pp. 312–366.Google Scholar
[11] Siegel, C. L. “A simple proof of Mathematika 1 (1954), p. 4.Google Scholar
[12] Siegel, C. L. Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1962.Google Scholar
[13] Weil, A. “Sur une formule classique,” J. Math. Soc. Japan 20 (1968), pp. 399–402.Google Scholar