- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Average values on the Jacobian variety of a hyperelliptic curve Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 333-349 https://doi.org/10.4134/BKMS.b180167Published online 2019 Mar 01 Jiman Chung, Bo-Hae Im Chung-Ang University; KAIST Abstract : We give explicitly an average value formula under the multi\-plication-by-$2$ map for the $x$-coordinates of the $2$-division points $D$ on the Jacobian variety $J(C)$ of a hyperelliptic curve $C$ with genus $g$ if $2D \equiv 2P-2\infty \pmod{\mathrm{Pic}(C)}$ for $P=(x_P, y_P) \in C$ with $y_P \ne 0$. Moreover, if $g=2$, we give a more explicit formula for $D$ such that $2D \equiv P-\infty \pmod{\mathrm{Pic}(C)}$. Keywords : Jacobian variety, hyperelliptic curve MSC numbers : Primary 11G05 Full-Text :