scholarly journals On Drinfeld Modular Curves with Many Rational Points over Finite Fields

2002 ◽  
Vol 8 (4) ◽  
pp. 434-443
Author(s):  
Andreas Schweizer
Keyword(s):  
Finite Fields ◽  
Rational Points ◽  
Modular Curves ◽  
Drinfeld Modular Curves

scholarly journals Construction of elliptic curves with cyclic groups over prime fields

2006 ◽  
Vol 73 (2) ◽  
pp. 245-254 ◽  
Author(s):  
Naoya Nakazawa
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Function Field ◽  
Modular Group ◽  
Modular Function ◽  
Invariant Function ◽  
Rational Points ◽  
Modular Invariant ◽  
Cyclic Groups ◽  
Prime Fields

The purpose of this article is to construct families of elliptic curves E over finite fields F so that the groups of F-rational points of E are cyclic, by using a representation of the modular invariant function by a generator of a modular function field associated with the modular group Γ0(N), where N = 5, 7 or 13.

On the curve Yn = Xℓ(Xm + 1) over finite fields

2019 ◽  
Vol 19 (2) ◽  
pp. 263-268 ◽  
Author(s):  
Saeed Tafazolian ◽  
Fernando Torres
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Plane Curve ◽  
Rational Points ◽  
Weil Bound

Abstract Let 𝓧 be the nonsingular model of a plane curve of type yn = f(x) over the finite field F of order q2, where f(x) is a separable polynomial of degree coprime to n. If the number of F-rational points of 𝓧 attains the Hasse–Weil bound, then the condition that n divides q+1 is equivalent to the solubility of f(x) in F; see [20]. In this paper, we investigate this condition for f(x) = xℓ(xm+1).

scholarly journals Counting Rational Points of an Algebraic Variety over Finite Fields

2019 ◽  
Vol 74 (1) ◽  
Author(s):  
Shuangnian Hu ◽  
Xiaoer Qin ◽  
Junyong Zhao
Keyword(s):  
Finite Fields ◽  
Algebraic Variety ◽  
Rational Points ◽  
Counting Rational Points

scholarly journals Towers of function fields over finite fields corresponding to elliptic modular curves

2012 ◽  
Vol 18 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Takehiro Hasegawa ◽  
Miyoko Inuzuka ◽  
Takafumi Suzuki
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Modular Curves ◽  
Towers Of Function Fields

scholarly journals Congruences for rational points on varieties over finite fields

2005 ◽  
Vol 333 (4) ◽  
pp. 797-809 ◽  
Author(s):  
N. Fakhruddin ◽  
C. S. Rajan
Keyword(s):  
Finite Fields ◽  
Rational Points

Rational torsion of generalized Jacobians of modular and Drinfeld modular curves

2019 ◽  
Vol 31 (3) ◽  
pp. 647-659
Author(s):  
Fu-Tsun Wei ◽  
Takao Yamazaki
Keyword(s):  
Prime Power ◽  
Analogous Result ◽  
Power Level ◽  
Modular Curves ◽  
Generalized Jacobian ◽  
Torsion Points ◽  
Modular Curve ◽  
Generalized Jacobians ◽  
Drinfeld Modular Curves ◽  
Primary Torsion

Abstract We consider the generalized Jacobian {\widetilde{J}} of the modular curve {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the {\mathbb{Q}} -rational torsion points on {\widetilde{J}} up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on {\widetilde{J}} and its Eisenstein property.

Sign in / Sign up

Export Citation Format

Share Document