p-adic L-functions and rational points on elliptic curves with complex multiplication.
Karl Rubin (1992)
Inventiones mathematicae
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Displaying similar documents to “The polynomial and elliptic curves of conductor 11”
p-adic L-functions and rational points on elliptic curves with complex multiplication.
-integral solutions to a Weierstrass equation
Benjamin M. M. de Weger (1997)
Journal de théorie des nombres de Bordeaux
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The rational solutions with as denominators powers of to the elliptic diophantine equation are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term (-) unit equations with special properties, that are solved by linear forms in real and -adic logarithms.
On p-adic L-functions Associated to Elliptic Curves.
Stephen Lichtenbaum (1980)
Inventiones mathematicae
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L-series and their 2-adic valuations at s = 1 attached to CM elliptic curves
Derong Qiu, Xianke Zhang (2002)
Acta Arithmetica
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Elliptic curves and class fields of real quadratic fields: Algorithms and evidence.
Darmon, Henri, Green, Peter (2002)
Experimental Mathematics
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-integral points on elliptic curves - Notes on a paper of B. M. M. de Weger
Emanuel Herrmann, Attila Pethö (2001)
Journal de théorie des nombres de Bordeaux
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In this paper we give a much shorter proof for a result of B.M.M de Weger. For this purpose we use the theory of linear forms in complex and -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.
Some functions related to the derivatives of the L-series of an elliptic curve at s=1
M. J. Razar (1980)
Mémoires de la Société Mathématique de France
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Zero-cycles on products of elliptic curves over p-adic fields
Takashi Takemoto (2011)
Acta Arithmetica
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Computation of -adic heights and log convergence.
Mazur, Barry, Stein, William, Tate, John (2007)
Documenta Mathematica
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On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.
B. Mazur, J. Tate, J. Teitelbaum (1986)
Inventiones mathematicae
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A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
John L. Boxall (1986)
Annales de l'institut Fourier
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In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.