A construction of curves over finite fields
Arnaldo Garcia, Luciane Quoos (2001)
Acta Arithmetica
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Displaying similar documents to “Constructions of plane curves with many points”
A construction of curves over finite fields
Trivial points on towers of curves
Xavier Xarles (2013)
Journal de Théorie des Nombres de Bordeaux
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In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Non-existence of points rational over number fields on Shimura curves
Keisuke Arai (2016)
Acta Arithmetica
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Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Pencils of irreducible rational curves and plane Jacobian conjecture
Nguyen Van Chau (2011)
Annales Polonici Mathematici
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In certain cases the invertibility of a polynomial map F = (P,Q): ℂ²→ ℂ² can be characterized by the irreducibility and the rationality of the curves aP+bQ = 0, (a:b) ∈ ℙ¹.
The genus of curves over finite fields with many rational points.
Fernando Torres, Rainer Fuhrmann (1996)
Manuscripta mathematica
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On certain plane curves with many integral points.
Rodriguez Villegas, Fernando, Voloch, José Felipe (1999)
Experimental Mathematics
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Appendix to "Plücker conditions on plane rational curves": Families of rational plane curves.
Stein Arild Stromme (1984)
Mathematica Scandinavica
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On a class of rational cuspidal plane curves.
Hubert Flenner, Mikhail Zaidenberg (1996)
Manuscripta mathematica
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Points on Shimura curves over fields of even degree.
S. Kamienny (1990)
Mathematische Annalen
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Hyperelliptic plane curves of type .
Sakai, Fumio, Salem, Mohammad, Tono, Keita (2010)
Beiträge zur Algebra und Geometrie
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Rational 1- and 2-cuspidal plane curves.
Fenske, Torsten (1999)
Beiträge zur Algebra und Geometrie
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Some Estimates for Plane Cuspidal Curves
S. Y. Orevkov, M. G. Zaidenberg (1993)
Cours de l'institut Fourier
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On the height constant for curves of genus two, II
Michael Stoll (2002)
Acta Arithmetica
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Certain maximal curves and Cartier operators
Arnaldo Garcia, Saeed Tafazolian (2008)
Acta Arithmetica
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Some curves of prescribed rim-types
B. B. Epps (1973)
Colloquium Mathematicae
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On new definitions and interpretations of union, hyperasymptotic and hypernormal curves in the three-dimensional Euclidean space
H. K. N. Trivedi, S. C. Rastogi (1973)
Annales Polonici Mathematici
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Divisors on general curves and cuspidal rational curves.
D. Eisenbud, J. Harris (1983)
Inventiones mathematicae
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Congruent numbers over real number fields
Tomasz Jędrzejak (2012)
Colloquium Mathematicae
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It is classical that a natural number n is congruent iff the rank of ℚ -points on Eₙ: y² = x³-n²x is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.