Variance of point-counts for families of cubic curves over $\mathbb{F}_p$ and Jacobsthal sums

Bogdan Nica

Variance of point-counts for families of cubic curves over $\mathbb{F}_p$ and Jacobsthal sums

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arxiv 2504.15505 v1 pith:KV5UP6MF submitted 2025-04-22 math.NT

Bogdan Nica This is my paper · ORCID

classification math.NT

keywords cubiccurvesfamiliesjacobsthalsumsvariancealongcomputations

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We give explicit computations for the variance of the number of points along one-parameter families of cubic curves. We highlight evaluations of variances that involve Jacobsthal sums.

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On quadratic character sums over quartics
math.NT 2025-07 accept novelty 6.0 of 10

The paper derives a master double-counting formula and several quartic-to-cubic transformation identities for quadratic character sums over finite fields.

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