On the average value of the canonical height in higher dimensional families of elliptic curves
Wei Pin Wong
Acta Arithmetica, Tome 166 (2014), p. 101-128 / Harvested from The Polish Digital Mathematics Library
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Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height ĥEω of the specialized elliptic curve Eω with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient (ĥEω(Pω))/h(ω) over all nontorsion P ∈ E(K).

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:279115 
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     title = {On the average value of the canonical height in higher dimensional families of elliptic curves},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {101-128},
     zbl = {1316.11048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-2-1}
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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) pp. 101-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-2-1/