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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 of the specialized elliptic curve with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient over all nontorsion P ∈ E(K).
Wei Pin Wong. "On the average value of the canonical height in higher dimensional families of elliptic curves." Acta Arithmetica 166.2 (2014): 101-128. <http://eudml.org/doc/279115>.
@article{WeiPinWong2014, abstract = {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).}, author = {Wei Pin Wong}, journal = {Acta Arithmetica}, keywords = {height function; elliptic curves; function field}, language = {eng}, number = {2}, pages = {101-128}, title = {On the average value of the canonical height in higher dimensional families of elliptic curves}, url = {http://eudml.org/doc/279115}, volume = {166}, year = {2014}, }
TY - JOUR AU - Wei Pin Wong TI - On the average value of the canonical height in higher dimensional families of elliptic curves JO - Acta Arithmetica PY - 2014 VL - 166 IS - 2 SP - 101 EP - 128 AB - 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). LA - eng KW - height function; elliptic curves; function field UR - http://eudml.org/doc/279115 ER -