References
Abramowitz, M., Stegun, I.: Handbook of mathematical functions. New York: Dover 1965
Doi, K., Naganuma, H.: On the functional equation of certain Dirichlet series. Inventiones math9, 1–14 (1969)
Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers.4th ed., Oxford: Clarendon Press 1965
Hecke, E.: Analytische Funktionen und algebraische Zahlen. II. Abh. aus dem Math. Seminar der Hamburgischen Univ.3, 213–236 (1924) (Mathematische Werke, pp. 381–404. Göttingen: Vandenhoeck & Ruprecht 1970)
Hecke, E.: Über die Darstellung der Determinante einer positiven quadratischen Form durch die Form, Vierteljahrschrift d. Naturforschenden Gesellschaft in Zürich85, 64–70 (1940) (Mathematische Werke, pp. 782–788 Göttingen: Vandenhoeck & Ruprecht 1970)
Jacquet, H.: Automorphic Functions onGL(2). Part II. Lecture Notes in Mathematics278, Berlin-Heidelberg-New York, Springer 1972
Lehner, J.: Discontinuous groups and automorphic functions. AMS, Providence 1964
Naganuma, H.: On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “Neben”-type and Hilbert modular forms over a real quadratic field. J. Math. Soc. Japan25, 547–555 (1973)
Ogg, A.: Survey of modular functions of one variable. Modular functions of one variable I. Lecture Notes in Mathematics320, pp. 1–36. Berlin-Heidelberg-New York: Springer 1973
Rankin, R.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions. I. Proc. Camb. Phil. Soc.35, 351–356 (1939)
Siegel, C. L.: Berechnung von Zetafunktionen an ganzzahligen Stellen. Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl.10, 87–102 (1969)
Zagier, D.: Formes modulaires à une et deux variables. C. R. Acad. Sci. Paris A,279, 683–686 (1974)
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Zagier, D. Modular forms associated to real quadratic fields. Invent Math 30, 1–46 (1975). https://doi.org/10.1007/BF01389846
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DOI: https://doi.org/10.1007/BF01389846