Eisenstein series of weight 3/2. I

Pei, Ting Yi

doi:10.1090/S0002-9947-1982-0675068-1

Eisenstein series of weight $3/2$. I
HTML articles powered by AMS MathViewer

by Ting Yi Pei

Trans. Amer. Math. Soc. 274 (1982), 573-606

DOI: https://doi.org/10.1090/S0002-9947-1982-0675068-1

PDF | Request permission

Abstract:

We prove that in the space of elliptic modular forms with weight 3/2, the orthogonal complement of the subspace of cusp forms with respect to the Petersson inner product is generated by Eisenstein series in some special cases.

References

H. Cohen and J. Oesterlé, Dimensions des espaces de formes modulaires, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977, pp. 69–78 (French). MR 0472703

Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik

5

Konstruktion ganzer Modulformen halbzahliger Dimension mit

-Multiplikatoren in einer und zwei Variablen

12

Über die Entwicklungskoeftizienten der ganzen Modulformen und ihre Bedentung für die Zahlentheorie

8

J.-P. Serre and H. M. Stark, Modular forms of weight $1/2$, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977, pp. 27–67. MR 0472707
Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481. MR 332663, DOI 10.2307/1970831
Goro Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), no. 1, 79–98. MR 382176, DOI 10.1112/plms/s3-31.1.79
Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. MR 0314766
Jacob Sturm, Special values of zeta functions, and Eisenstein series of half integral weight, Amer. J. Math. 102 (1980), no. 2, 219–240. MR 564472, DOI 10.2307/2374237