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Root numbers and algebraic points on elliptic surfaces with base $\mathbb{P}^1$
Gregory R. Grant and Elisabetta Manduchi
Source: Duke Math. J. Volume 89, Number 3
(1997), 413-422.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077241202
Mathematical Reviews number (MathSciNet): MR1470337
Zentralblatt MATH identifier: 0907.14012
Digital Object Identifier: doi:10.1215/S0012-7094-97-08918-3
References
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[7] D. E. Rohrlich, Galois theory, elliptic curves, and root numbers, Compositio Math. 100 (1996), no. 3, 311–349.
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[9] T. Shioda, An explicit algorithm for computing the Picard number of certain algebraic surfaces, Amer. J. Math. 108 (1986), no. 2, 415–432.
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JSTOR: links.jstor.org
[10] J. H. Silverman, Integral points on curves and surfaces, Number theory (Ulm, 1987), Lecture Notes in Math., vol. 1380, Springer, New York, 1989, pp. 202–241.
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[11] J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 151, Springer-Verlag, New York, 1994.
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[12] J. T. Tate, Number theoretic background, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3–26.
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