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Gross, Benedict H.
[Rohrlich, D. E.]

On the periods of Abelian integrals and a formula of Chowla and Selberg. With an appendix by David E. Rohrlich. (English) Zbl 0418.14023

Invent. Math. 45, 193-211 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 4 Reviews
Cited in 64 Documents

MSC:

14K22 Complex multiplication and abelian varieties
14H10 Families, moduli of curves (algebraic)
14H25 Arithmetic ground fields for curves
11G15 Complex multiplication and moduli of abelian varieties

Keywords:

periods of an elliptic curve; complex multiplications; algebraic point; moduli space for abelian varieties with complex multiplications; Gauss- Manin connection; computation of the periods

Citations:

Zbl 0166.052; Zbl 0342.14020
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Full Text: DOI EuDML

References:

[1] [B-B] Baily, W., Borel, A.: Compactification of Arithmetic Quotients of Bounded Symmetric Domains. Ann. of Math.84, 442-528 (1966) · Zbl 0154.08602 · doi:10.2307/1970457
[2] [C-S] Chowla, S., Selberg, A.: On Epstein’s Zeta-function. J. Crelle227, 86-110 (1967) · Zbl 0166.05204
[3] [Da] Damerell, R.M.:L-functions of Elliptic Curves with Complex Multiplication I. and II. Acta. Arith.17, 287-301 (1970);19, 311-317 (1971) · Zbl 0209.24603
[4] [D1] Deligne, P.: Equations Différentielles à Points Singuliers Réguliers. Lecture Notes 163, Berlin, Heidelberg, New York: Springer (1970)
[5] [D2] Deligne, P.: Letter to D. Zagier. July 18, 1977
[6] [D3] Deligne, P.: Sommes Trigonométriques. Cohomology Etale (SGA 41/2), Springer Lecture Notes 569, Berlin, Heidelberg, New York: Springer (1977)
[7] [D4] Deligne, P.: Théorie de Hodge II. Publ. Math. IHES40, 5-57 (1972)
[8] [K-O] Katz, N., Oda, T.: On the Differentiation of deRham Cohomology Classes with Respect to Parameters. J. Math. Kyoto Univ.8-2, 199-213 (1968) · Zbl 0165.54802
[9] [Se] Serre, J.-P.: Prolongement de Faisceaux Analytiques Cohérents. Ann. Inst. Fourier.16-1, 363-374 (1966) · Zbl 0144.08003
[10] [S1] Shimura, G.: Moduli and Fibre Systems of Abelian Varieties. Ann. of Math.83-2, 294-338 (1966) · Zbl 0141.37503 · doi:10.2307/1970434
[11] [S2] Shimura, G.: On Analytic Families of Polarized Abelian Varieties and Automorphic Functions. Ann. of Math.78, 149-192 (1963) · Zbl 0142.05402 · doi:10.2307/1970507
[12] [S3] Shimura, G.: On Elliptic Curves with Complex Multiplication as Factors of the Jacobian of Modular Function Fields. Nagoya Math. J.43, 199-208 (1971) · Zbl 0225.14015
[13] [Wa] Waldschmidt, M.: Les Travaux de C.V. ?udnovskiî sur les Nombres Transcendants. Sém. Bourbaki 488 (1975/1976), Lecture Notes 567, Berlin, Heidelberg, New York: Springer (1977)
[14] [W1] Weil, A.: Abelian Varieties and the Hodge Ring (Preprint)
[15] [W2] Weil, A.: Sommes de Jacobi et Caractères de Hecke Nach. Akad. Wiss. Göttingen1, 1-14 (1974)
[16] [W3] Weil, A.: Sur les Périodes des Intégrales Abéliennes. Comm. Pure App. Math.29, 813-819 (1976) · Zbl 0342.14020 · doi:10.1002/cpa.3160290620
[17] [W4] Weil, A.: Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann.168, 149-156 (1967) · Zbl 0158.08601 · doi:10.1007/BF01361551
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