Cyclicity and generation of points mod \(p\) on elliptic curves

DOI10.1007/BF01231502zbMath0731.14011MaRDI QIDQ807692

M. Ram Murty, Rajiv Gupta

Publication date: 1990

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143803

zbMATH Keywords

sieve theorycyclicity of group of rational pointsprimitive root conjecture

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Applications of sieve methods (11N36)

Related Items

Parametric families of elliptic curves with cyclic \(\mathbb F_p\)-rational points groups ⋮ Cyclicity of elliptic curves modulo primes in arithmetic progressions ⋮ Artin's conjecture for abelian varieties ⋮ Bounded gaps between primes with a given primitive root. II ⋮ Cyclic components of quotients of abelian varieties mod \(p\) ⋮ Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height ⋮ Unnamed Item ⋮ 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 ⋮ 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 ⋮ Reductions of points on elliptic curves ⋮ 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 \(p\) ⋮ Positivity of constants related to elliptic curves ⋮ Construction of elliptic curves with cyclic groups over prime fields ⋮ Cyclicity statistics for elliptic curves over finite fields ⋮ On the cyclicity of the group of \({\mathbb F}_p\)-rational points of non-CM elliptic curves

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• Primes in arithmetic progressions