Number of rational places of subfields of the function field of the Deligne-Lusztig curve of Ree type
Emrah Çakçak, Ferruh Özbudak (2005)
Acta Arithmetica
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Emrah Çakçak, Ferruh Özbudak (2005)
Acta Arithmetica
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Dimitrios Poulakis (2003)
Acta Arithmetica
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Rusin, David J. (1998)
The New York Journal of Mathematics [electronic only]
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Soukenka, Martin
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J. Achari (1978)
Matematički Vesnik
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J. MacLeod, Allan (2008)
Annales Mathematicae et Informaticae
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Ayhan Günaydın, Philipp Hieronymi (2011)
Fundamenta Mathematicae
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We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.
J. Achari (1979)
Publications de l'Institut Mathématique
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P. Field (1933)
Mathematische Zeitschrift
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Matusevich, Laura Felicia (2000)
Beiträge zur Algebra und Geometrie
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Alf Bjorn Aure (1984)
Mathematica Scandinavica
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J. Siciak (1962)
Annales Polonici Mathematici
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M. R. Gonzalez-Dorrego (2006)
Annales Polonici Mathematici
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Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.
Paul Monsky (1992)
Mathematische Zeitschrift
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