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Transactions of the American Mathematical Society

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Spherical polynomials and the periods of a certain modular form


Author: David Kramer
Journal: Trans. Amer. Math. Soc. 294 (1986), 595-605
MSC: Primary 11F11; Secondary 11F66
DOI: https://doi.org/10.1090/S0002-9947-1986-0825724-0
MathSciNet review: 825724
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Abstract: The space of cusp forms on $ {\text{S}}{{\text{L}}_2}({\mathbf{Z}})$ of weight $ 2k$ is spanned by certain modular forms with rational periods.


References [Enhancements On Off] (What's this?)

  • [1] Erich Hecke, Zur Theorie der Elliptischen Modulfunktionen, Math. Ann. 97 (1926), 210-242. Number 23 in Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959. MR 1512360
  • [2] -, Analytische Funktionen und Algebraische Zahlen, Zweiter Teil, Abh. Math. Sem. Univ. Hamburg. 3 (1924), 13-236. Number 20 in Mathematische Werke.
  • [3] Svetlana Katok, Modular forms associated to closed geodesics and arithmetic applications, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 177-179. MR 741734 (85h:11026)
  • [4] Winfried Kohnen, Beziehungen Zwischen Modulformen Halbganzen Gewichts und Modulformen Ganzen Gewichts, Schriften Nr. 131, Bonner Math., Bonn, 1981. MR 633060 (83b:10026)
  • [5] Winfried Kohnen and Don Zagier, Modular forms with rational periods (to appear). MR 803368 (87h:11043)
  • [6] -, Values of $ L$-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), 175-198. MR 629468 (83b:10029)
  • [7] David Kramer, Applications of Gauss's theory of binary quadratic forms to zeta functions and modular forms, Trans. Amer. Math. Soc. (to appear).
  • [8] Andrew Ogg, Modular forms and Dirichlet series, Benjamin, New York, 1969. MR 0256993 (41:1648)
  • [9] Serge Lang, Introduction to modular forms, Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0429740 (55:2751)
  • [10] Carl L. Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1969, 87-102. MR 0252349 (40:5570)
  • [11] Don Zagier, A Kronecker limit formula for real quadratic fields, Math. Ann. 213 (1975), 153-184. MR 0366877 (51:3123)
  • [12] -, Zetafunktionen und Quadratische Körper, Springer-Verlag, Berlin-Heidelberg-New York, 1981. MR 631688 (82m:10002)
  • [13] -, Modular forms associated to real quadratic fields, Invent. Math. 30 (1975), 1-46. MR 0382174 (52:3062)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0825724-0
Article copyright: © Copyright 1986 American Mathematical Society

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