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 Average values on the Jacobian variety of a hyperelliptic curve Bull. Korean Math. Soc.Published online 2019 Mar 19 Jiman Chung, and Bo-Hae Im Chung-Ang University, KAIST Abstract : We give explicitly an average value formula for the $x$-coordinates of the $2$-division points on the Jacobian variety of a hyperelliptic curve under the multiplication-by-$2$ map. Keywords : Jacobian variety, hyperelliptic curve MSC numbers : 11G05 Full-Text :