On the average value of the canonical height in higher dimensional families of elliptic curves

• Autorzy: Wei Pin Wong
• Języki publikacji: EN

Abstrakty

EN

Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height $ĥ_{E_ω}$ of the specialized elliptic curve $E_ω$ with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient $(ĥ_{E_ω}(P_ω))/h(ω)$ over all nontorsion P ∈ E(K).

Kategorie tematyczne

• 11G50: Heights
• 11G05: Elliptic curves over global fields
• 14G40: Arithmetic varieties and schemes; Arakelov theory; heights

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 2
• Strony: 101-128

Daty

wydano

2014

Twórcy

autor

Wei Pin Wong

• Mathematics Department, Box 1917, Brown University, Providence, RI 02912, U.S.A.

Identyfikatory

DOI

10.4064/aa166-2-1