Spherical polynomials and the periods of a certain modular form

Spherical polynomials and the periods of a certain modular form
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by David Kramer PDF

Trans. Amer. Math. Soc. 294 (1986), 595-605 Request permission

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

E. Hecke, Zur Theorie der elliptischen Modulfunktionen, Math. Ann. 97 (1927), no. 1, 210–242 (German). MR 1512360, DOI 10.1007/BF01447866

Analytische Funktionen und Algebraische Zahlen, Zweiter Teil

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Svetlana Katok, Modular forms associated to closed geodesics and arithmetic applications, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 177–179. MR 741734, DOI 10.1090/S0273-0979-1984-15257-1
Winfried Kohnen, Beziehungen zwischen Modulformen halbganzen Gewichts und Modulformen ganzen Gewichts, Bonner Mathematische Schriften [Bonn Mathematical Publications], vol. 131, Universität Bonn, Mathematisches Institut, Bonn, 1981 (German). Dissertation, Rheinische Friedrich-Wilhelms-Universität, Bonn, 1980. MR 633060
W. Kohnen and D. Zagier, Modular forms with rational periods, Modular forms (Durham, 1983) Ellis Horwood Ser. Math. Appl.: Statist. Oper. Res., Horwood, Chichester, 1984, pp. 197–249. MR 803368
W. Kohnen and D. Zagier, Values of $L$-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), no. 2, 175–198. MR 629468, DOI 10.1007/BF01389166

Applications of Gauss’s theory of binary quadratic forms to zeta functions and modular forms

Andrew Ogg, Modular forms and Dirichlet series, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0256993
Serge Lang, Introduction to modular forms, Grundlehren der Mathematischen Wissenschaften, No. 222, Springer-Verlag, Berlin-New York, 1976. MR 0429740
Carl Ludwig Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1969 (1969), 87–102 (German). MR 252349
Don Zagier, A Kronecker limit formula for real quadratic fields, Math. Ann. 213 (1975), 153–184. MR 366877, DOI 10.1007/BF01343950
D. B. Zagier, Zetafunktionen und quadratische Körper, Hochschultext [University Textbooks], Springer-Verlag, Berlin-New York, 1981 (German). Eine Einführung in die höhere Zahlentheorie. [An introduction to higher number theory]. MR 631688
Don Zagier, Modular forms associated to real quadratic fields, Invent. Math. 30 (1975), no. 1, 1–46. MR 382174, DOI 10.1007/BF01389846