A mean value formula for elliptic curves
Rongquan Feng, Hongfeng Wu
TL;DR
This paper establishes a mean value formula for elliptic curves, showing that the average x-coordinate of n-division points equals the original point's x-coordinate, and the average y-coordinate is n times the original y-coordinate.
Contribution
It introduces a novel mean value formula for elliptic curves relating points and their n-division points, providing new insights into their geometric properties.
Findings
Average x-coordinate of n-division points equals original x-coordinate
Average y-coordinate of n-division points is n times the original y-coordinate
Provides a new formula connecting points on elliptic curves
Abstract
It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its n-division points is n times of its y-coordinate.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Cryptography and Residue Arithmetic