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- Title
Reductions of points on elliptic curves.
- Abstract
Let E be an elliptic curve defined over Q. Let Γ be a subgroup of rank r of the group of rational points E(Q) of E. For any prime p of good reduction, let Γ be the reduction of Γ modulo p. Under certain standard assumptions, we prove thatfor almost all primes p (i.e. for a set of primes of density one), we have Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where ƒ (x) is any function such that ƒ (x) → ∞, at an arbitrary slow speed, as x → ∞. This provides additional evidence in support of a conjecture of Lang and Trotter from 1977.
- Subjects
ELLIPTIC curves; RATIONAL points (Geometry); MATHEMATICAL logic; ALGEBRAIC curves; MATHEMATICAL functions
- Publication
Mathematische Annalen, 2010, Vol 347, Issue 2, p365
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-009-0433-6