×

zbMATH — the first resource for mathematics

Modular forms associated to real quadratic fields. (English) Zbl 0308.10014

MSC:
11F27 Theta series; Weil representation; theta correspondences
11F12 Automorphic forms, one variable
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Abramowitz, M., Stegun, I.: Handbook of mathematical functions. New York: Dover 1965 · Zbl 0171.38503
[2] Doi, K., Naganuma, H.: On the functional equation of certain Dirichlet series. Inventiones math9, 1-14 (1969) · Zbl 0182.54301
[3] Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers.4th ed., Oxford: Clarendon Press 1965 · Zbl 0020.29201
[4] 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) · JFM 50.0111.01
[5] 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) · Zbl 0023.22501
[6] Jacquet, H.: Automorphic Functions onGL(2). Part II. Lecture Notes in Mathematics278, Berlin-Heidelberg-New York, Springer 1972 · Zbl 0243.12005
[7] Lehner, J.: Discontinuous groups and automorphic functions. AMS, Providence 1964 · Zbl 0178.42902
[8] 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) · Zbl 0259.10023
[9] 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
[10] Rankin, R.: Contributions to the theory of Ramanujan’s function ?(n) and similar arithmetical functions. I. Proc. Camb. Phil. Soc.35, 351-356 (1939) · Zbl 0021.39201
[11] Siegel, C. L.: Berechnung von Zetafunktionen an ganzzahligen Stellen. Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl.10, 87-102 (1969) · Zbl 0186.08804
[12] Zagier, D.: Formes modulaires à une et deux variables. C. R. Acad. Sci. Paris A,279, 683-686 (1974) · Zbl 0293.10013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.