Reductions of an elliptic curve with almost prime orders
Alina Carmen Cojocaru (2005)
Acta Arithmetica
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Alina Carmen Cojocaru (2005)
Acta Arithmetica
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Sheldon Kamienny (1986)
Bulletin de la Société Mathématique de France
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Bas Edixhoven (1993-1994)
Séminaire Bourbaki
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Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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David E. Rohrlich (1993)
Compositio Mathematica
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J.F. Voloch (1988)
Bulletin de la Société Mathématique de France
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Dorian Goldfeld, Lucien Szpiro (1995)
Compositio Mathematica
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Franz Lemmermeyer (2003)
Acta Arithmetica
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Noboru Aoki (2004)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Min Sha, Igor E. Shparlinski (2015)
Acta Arithmetica
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We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of...