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MR983456 11G40 (11F11 11F46 11F67)
Bump, Daniel; Friedberg, Solomon; Hoffstein, Jeffrey A nonvanishing theorem for derivatives of automorphic $L$-functions with applications to elliptic curves. Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 89-93.
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