Cyclicity of CM elliptic curves modulo 𝑝

DOI10.1090/S0002-9947-03-03283-5zbMath1021.11019OpenAlexW1976171182MaRDI QIDQ4806452

Alina Carmen Cojocaru

Publication date: 14 May 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03283-5

zbMATH Keywords

complex multiplicationapplications of sieve methodscyclicity of elliptic curves modulo \(p\)

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Applications of sieve methods (11N36) Density theorems (11R45)

Related Items (19)

Cyclicity of elliptic curves modulo primes in arithmetic progressions ⋮ Bounded gaps between primes with a given primitive root. II ⋮ Averages of elliptic curve constants ⋮ Cyclicity of CM elliptic curves modulo 𝑝 ⋮ Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height ⋮ Unnamed Item ⋮ Small exponent point groups on elliptic curves ⋮ The average exponent of elliptic curves modulo \(p\) ⋮ Cyclic reduction densities for elliptic curves ⋮ The distribution and growth of the elementary divisors of the reductions of an elliptic curve over a function field ⋮ On Artin's conjecture for CM elliptic curves ⋮ Primes, elliptic curves and cyclic groups ⋮ Cyclicity and exponents of CM elliptic curves modulo $p$ in short intervals ⋮ The distribution and density of cyclic groups of the reductions of an elliptic curve over a function field ⋮ An observation on the cyclicity of the group of the \(\mathbb F_p\)-rational points of Abelian surfaces ⋮ Square-free orders for CM elliptic curves modulo \(p\) ⋮ Cyclicity of elliptic curves modulo \(p\) and elliptic curve analogues of Linnik's problem ⋮ An analogue of the Siegel-Walfisz theorem for the cyclicity of CM elliptic curves mod \(p\) ⋮ Average of the first invariant factor of the reductions of abelian varieties of CM type

Cites Work

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• On Artin's conjecture
• An analogue of Artin's conjecture for Abelian extensions
• Quelques applications du théorème de densité de Chebotarev
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• On the cyclicity of the group of \({\mathbb F}_p\)-rational points of non-CM elliptic curves
• On the large sieve method in algebraic number fields
• Primitive points on elliptic curves
• Elliptic Curves Over Finite Fields. II
• Cyclicity of CM elliptic curves modulo 𝑝

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