Explicit variance formulas for point counts of one-parameter families of cubic curves over F_p are derived, with several residual sums evaluated using Jacobsthal sums.
Birch: How the number of points of an elliptic curve over a fixed prime field varies, J
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Variance of point-counts for families of cubic curves over $\mathbb{F}_p$ and Jacobsthal sums
Explicit variance formulas for point counts of one-parameter families of cubic curves over F_p are derived, with several residual sums evaluated using Jacobsthal sums.