Analogues of Lehmer's conjecture in positive characteristic

Details Analogues of Lehmer's conjecture in positive characteristic Analogues of Lehmer's conjecture in positive characteristic

2000-11-15

arxiv.org/abs/math/0011102v6

Mathematics

Number Theory

revised version

Scientific paper

Let $C$ be a smooth projective irreducible curve defined over a finite field $\mathbb{F}_q$ and $K=\mathbb{F}_q(C)$. Let $A\subset K$ be the ring of functions regular outside a fixed place $\infty$ of $K$. Let $\phi:A\to\text{End}(\mathbb{G}_a)$ be a Drinfeld $A$-module of rank $r$ defined over a finite extension $L$ of $K$ and $\hat{h}_{\phi}$ its canonical height. Given a non-torsion point $\alpha$ of $\phi$ of degree $d$ over $K$, we prove that $\hat{h}_{\phi}(\alpha)\ge 1/d$. A similar statement is proved for the canonical height of a point of infinite order of a non-constant semi-stable elliptic curve defined over $K$, with the absolute constant 1 replaced by a constant depending on the elliptic curve.

Affiliated with

Also associated with

No associations

Rating

Analogues of Lehmer's conjecture in positive characteristic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analogues of Lehmer's conjecture in positive characteristic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analogues of Lehmer's conjecture in positive characteristic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-251339