Geodesic
On the average value of the canonical height in higher dimensional families of elliptic curves
Wei Pin Wong1
1 Mathematics Department Box 1917 Brown University Providence, RI 02912, U.S.A.
Acta Arithmetica, Tome 166 (2014) no. 2, pp. 101-128

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Given an elliptic curve $E$ over a function field $K=\mathbb {Q}(T_1, \ldots , T_n)$, we study the behavior of the canonical height $\hat{h}_{E_\omega }$ of the specialized elliptic curve $E_\omega $ with respect to the height of $\omega \in \mathbb {Q}^n$. We prove that there exists a uniform nonzero lower bound for the average of the quotient ${\hat{h}_{E_\omega }(P_\omega )}/{h(\omega )}$ over all nontorsion $P \in E(K)$.
DOI : 10.4064/aa166-2-1
Keywords: given elliptic curve function field mathbb ldots study behavior canonical height hat omega specialized elliptic curve omega respect height omega mathbb prove there exists uniform nonzero lower bound average quotient hat omega omega omega nontorsion

Wei Pin Wong 1

1 Mathematics Department Box 1917 Brown University Providence, RI 02912, U.S.A. 
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Wei Pin Wong. On the average value of the canonical height in
 higher dimensional families of elliptic curves. Acta Arithmetica, Tome 166 (2014) no. 2, pp. 101-128. doi: 10.4064/aa166-2-1

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