More Points Than Expected on Curves over Finite Field Extensions

Bradley W. Brock, Andrew Granville

Type: Article

Publication Date: 2001-01-01

Citations: 27

DOI: https://doi.org/10.1006/ffta.2000.0308

View Publication

Locations

Finite Fields and Their Applications - View

Similar Works

Action	Title	Year	Authors
+	The average number of torsion points on elliptic curves	2013	Hsiu-Lien Huang
+ PDF Chat	Improved upper bounds for the number of points on curves over finite fields	2003	Everett W. Howe Kristin Lauter
+	Fields generated by points on superelliptic curves	2021	Lea Beneish Christopher Keyes
+	Fields generated by points on superelliptic curves	2021	Lea Beneish Christopher Keyes
+	Lower bounds on the maximal number of rational points on curves over finite fields	2022	Jonas Bergström Everett W. Howe Elisa Lorenzo García Christophe Ritzenthaler
+	Rational points on curves over function fields	2013	Amílcar Pacheco Fabien Pazuki
+	Rational points on curves over function fields	2012	Amílcar Pacheco Fabien Pazuki
+ PDF Chat	Rational points on curves over function fields	2013	Amílcar Pacheco Fabien Pazuki
+ PDF Chat	Rational points on curves over function fields	2013	Amílcar Pacheco Fabien Pazuki
+ PDF Chat	Lower bounds on the maximal number of rational points on curves over finite fields	2023	Jonas Bergström Everett W. Howe Elisa Lorenzo García Christophe Ritzenthaler
+	Improved upper bounds for the number of rational points on algebraic curves over finite fields	1999	Kristin Lauter
+ PDF Chat	Average ranks of elliptic curves: Tension between data and conjecture	2007	Baur Bektemirov Barry Mazur William Stein Mark E. Watkins
+ PDF Chat	The number of rational points on Drinfeld modular varieties over finite fields	2006	Mihran Papikian
+	Algebraic curves with many points over the binary field	2007	Chaoping Xing Sze Ling Yeo
+	Improved upper bounds for the number of points on curves over finite fields	2002	Everett W. Howe Kristin Lauter
+	Improved upper bounds for the number of points on curves over finite fields	2002	Everett W. Howe Kristin Lauter
+ PDF Chat	How many rational points does a random curve have?	2013	Wei Ho
+	Modular curves with many points over finite fields	2023	Valerio Dose Guido Lido Pietro Mercuri Claudio Stirpe
+	Coverings of curves with asymptotically many rational points	1999	Wen-Ching Li Hiren Maharaj
+	On Curves with Many Rational Points over Finite Fields	2002	Arnaldo Garcia

Works That Cite This (27)

Action	Title	Year	Authors
+	Orbits of rational n-sets of projective spaces under the action of the linear group	2007	Ricard Martı́ Enric Nart
+	Twisted Klein curves modulo 2	2003	Iwan Duursma
+	Fluctuations in the number of points on smooth plane curves over finite fields	2010	Alina Bucur Chantal David Brooke Feigon Matilde Laĺın
+	CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS ARIZONA WINTER SCHOOL 2014: ARITHMETIC STATISTICS	2014	Chantal David Alina Bucur
+ PDF Chat	Traces, high powers and one level density for families of curves over finite fields	2017	Alina Bucur Edgar Costa Chantal David João Guerreiro David Lowry-Duda
+ PDF Chat	Odd moments for the trace of Frobenius and the Sato–Tate conjecture in arithmetic progressions	2024	Kathrin Bringmann Ben Kane Sudhir Pujahari
+ PDF Chat	Non-hyperelliptic curves of genus three over finite fields of characteristic two	2005	Enric Nart Christophe Ritzenthaler
+	Hyperelliptic curves and their invariants: Geometric, arithmetic and algorithmic aspects	2012	Reynald Lercier Christophe Ritzenthaler
+ PDF Chat	Counting curves over finite fields	2014	Gerard van der Geer
+	Computing binary curves of genus five	2023	Dušan Dragutinović

Works Cited by This (17)

Action	Title	Year	Authors
+	Formes modulaires et représentations e-adiques	2006	Pierre Deligne
+	Random Matrices, Frobenius Eigenvalues, and Monodromy	1998	Nicholas M. Katz Peter Sarnak
+	The number of regular semisimple classes of special linear and unitary groups	1998	Peter Fleischmann Ingo Janiszczak Reinhard Knörr
+	Frobenius–Schur Indicator and the Ubiquity of Brock–Granville Quadratic Excess	2001	Nicholas M. Katz
+	THE RATIONALITY OF MODULI SPACES OF HYPERELLIPTIC CURVES	1985	P. I. Katsylo
+	The symmetric cube	1996	Daniel Bump David Ginzburg Jeffrey Hoffstein
+	Abelian l-Adic Representations and Elliptic Curves	1997	Jean-Pierre Serre
+	How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies	1968	B. J. Birch
+	On the Holomorphy of Certain Dirichlet Series	1975	Goro Shimura
+	La conjecture de Weil. I	1974	Pierre Deligne