Quasi-equivalence of heights in algebraic function fields of one variable

Ruyong Feng, Shuang Feng, Li-Yong Shen

For points $(a,b)$ on an algebraic curve over a field $K$ with height $\mathfrak{h}$, the asymptotic relation between $\mathfrak{h}(a)$ and $\mathfrak{h}(b)$ has been extensively s…