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On the exponent of the group of points on elliptic curves in extension fields
- Intern. Math. Research Notices
"... Let E be an elliptic curve defined over Fq, a finite field of q elements. Furthermore, we consider ..."
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Cited by 5 (2 self)
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Let E be an elliptic curve defined over Fq, a finite field of q elements. Furthermore, we consider
Cyclicity of finite abelian varieties of type III, submitted. Available here: www2.math.kyushu-u.ac.jp/ virdol
"... Consider A an abelian variety of dimension r, defined over a number field F, such that EndF A ⊗ Q =EndAF ¯ ⊗ Q, with endomorphism algebra of type I or II in the Albert classification. Assume that A has potential good reduction everywhere. For ℘ a finite prime of F, we denote by F℘ the residue field ..."
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Cited by 1 (1 self)
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Consider A an abelian variety of dimension r, defined over a number field F, such that EndF A ⊗ Q =EndAF ¯ ⊗ Q, with endomorphism algebra of type I or II in the Albert classification. Assume that A has potential good reduction everywhere. For ℘ a finite prime of F, we denote by F℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A of type I and II, we obtain an asymptotic formula for the number of primes ℘ of F, with NF/Q ℘ ≤ x, for which Ā(F℘) has at most 2r −1 cyclic components.
AN ANALOGUE OF THE SIEGEL-WALFISZ THEOREM FOR THE CYCLICITY OF CM ELLIPTIC CURVES MOD p
"... Abstract. Let E be a CM elliptic curve defined over Q and of conductor N. We establish an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Our result resembles the classical Siegel-Walfisz theorem regar ..."
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Abstract. Let E be a CM elliptic curve defined over Q and of conductor N. We establish an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Our result resembles the classical Siegel-Walfisz theorem regarding the distribution of primes in arithmetic progressions. 1.
Cyclicity of finite CM abelian varieties
, 2012
"... Consider A an abelian variety over a number field F of dimension r, where r ≥ 1 is an integer. Assume that EndF ¯ A ⊗ Q = K, where K is a CM-field such that [K: Q] = 2r. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ..."
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Consider A an abelian variety over a number field F of dimension r, where r ≥ 1 is an integer. Assume that EndF ¯ A ⊗ Q = K, where K is a CM-field such that [K: Q] = 2r. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, we obtain an asymptotic formula for the number of primes ℘ of F, with NF/Q ℘ ≤ x, for which Ā(F℘) has at most 2r − 1 cyclic components.
Cyclicity of finite abelian varieties
, 2012
"... Consider A an abelian variety of dimension r, defined over a number field F. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A, we obtain an asymptoti ..."
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Consider A an abelian variety of dimension r, defined over a number field F. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A, we obtain an asymptotic formula for the number of primes ℘ of F, with NF/Q ℘ ≤ x, for which Ā(F℘) has at most 2r − 1 cyclic components.
