scholarly journals The Manin constant of elliptic curves over function fields

2010 ◽  
Vol 4 (5) ◽  
pp. 509-545 ◽  
Author(s):  
Ambrus Pál
Keyword(s):  
Elliptic Curves ◽  
Function Fields

scholarly journals Elliptic Curves with Large Rank over Function Fields

2002 ◽  
Vol 155 (1) ◽  
pp. 295 ◽  
Author(s):  
Douglas Ulmer
Keyword(s):  
Elliptic Curves ◽  
Function Fields ◽  
Large Rank

scholarly journals On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields

1971 ◽  
Vol 43 ◽  
pp. 199-208 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Elliptic Curves ◽  
Cusp Form ◽  
Mellin Transform ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Function Fields ◽  
Complex Multiplication ◽  
Modular Function ◽  
Imaginary Quadratic Field

1. As Hecke showed, every L-function of an imaginary quadratic field K with a Grössen-character γ is the Mellin transform of a cusp form f(z) belonging to a certain congruence subgroup Γ of SL2(Z). We can normalize γ so that

Erratum: "Prime numbre races for elliptic curves over function fields"

2021 ◽  
Vol 54 (5) ◽  
pp. 1353-1362
Author(s):  
Byungchul CHA ◽  
Daniel FIORILLI ◽  
Florent JOUVE
Keyword(s):  
Elliptic Curves ◽  
Function Fields

Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields

1995 ◽  
Vol 38 (2) ◽  
pp. 167-173 ◽  
Author(s):  
David A. Clark ◽  
Masato Kuwata
Keyword(s):  
Finite Field ◽  
Prime Ideal ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Function Field ◽  
Function Fields ◽  
Artin's Conjecture ◽  
Primitive Roots

AbstractLet k = Fq be a finite field of characteristic p with q elements and let K be a function field of one variable over k. Consider an elliptic curve E defined over K. We determine how often the reduction of this elliptic curve to a prime ideal is cyclic. This is done by generalizing a result of Bilharz to a more general form of Artin's primitive roots problem formulated by R. Murty.

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