Currently displaying 1 – 20 of 22

Showing per page

Order by Relevance | Title | Year of publication

On a dynamical Brauer–Manin obstruction

Liang-Chung Hsia;  Joseph Silverman — 2009

Journal de Théorie des Nombres de Bordeaux

Let ϕ : X → X be a morphism of a variety defined over a number field  K , let  V ⊂ X be a K -subvariety, and let  𝒪 ϕ ( P ) = { ϕ n ( P ) : n ≥ 0 } be the orbit of a point  P ∈ X ( K ) . We describe a local-global principle for the intersection  V ∩ 𝒪 ϕ ( P ) . This principle may be viewed as a dynamical analog of the Brauer–Manin obstruction. We show that the rational points of  V ( K ) are Brauer–Manin unobstructed for power maps on  ℙ 2 in two cases: (1)  V is a translate of a torus. (2)  V is a line and  P has a preperiodic coordinate. A key tool in the proofs is the classical...

Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves

Joseph H. Silverman — 2012

Journal de Théorie des Nombres de Bordeaux

A number of authors have proven explicit versions of Lehmer’s conjecture for polynomials whose coefficients are all congruent to  1 modulo  m . We prove a similar result for polynomials  f ( X ) that are divisible in  ( ℤ / m ℤ ) [ X ] by a polynomial of the form 1 + X + ⋯ + X n for some n ≥ ϵ deg ( f ) . We also formulate and prove an analogous statement for elliptic curves.

Page 1 Next

Download Results (CSV)