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The periods of Abelian varieties with complex multiplication and the spectral values of certain zeta functions. (English) Zbl 0458.14016

Mém. Soc. Math. Fr., Nouv. Sér. 2, 103-106 (1980).
For the entire collection see [Zbl 0441.00008].

MSC:

14K22 Complex multiplication and abelian varieties
11G15 Complex multiplication and moduli of abelian varieties
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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References:

[1] G. SHIMURA , On some arithmetic properties of modular forms of one and several variables , Ann. of Math. 102 ( 1975 ), 491-515. MR 58 #10758 | Zbl 0327.10028 · Zbl 0327.10028 · doi:10.2307/1971041
[2] G. SHIMURA , On the derivatives of theta functions and modular forms , Duke Math. J. 44 ( 1977 ), 365-387. Article | MR 57 #5911 | Zbl 0371.14023 · Zbl 0371.14023 · doi:10.1215/S0012-7094-77-04416-7
[3] G. SHIMURA , Automorphic forms and the periods of abelian varieties , J. Math. Soc. Japan, 31 ( 1979 ), 561-592. Article | MR 81j:10034 | Zbl 0456.10015 · Zbl 0456.10015 · doi:10.2969/jmsj/03130561
[4] G. SHIMURA , The arithmetic of certain zeta functions and automorphic forms on orthogonal groups , to appear in Ann. of Math., 110 ( 1980 ). MR 81g:10041 | Zbl 0438.12003 · Zbl 0438.12003 · doi:10.2307/1971202
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