Lea Beneish

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20242026

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math.NT2026

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11

Lea Beneish, Christopher Keyes

We establish an effective Bertini-type theorem for hypersurfaces $X_{f} : f = 0$ defined over a finite field $k$ for which $f$ has no linear factors over the algebraic closure $…

math.NT2025

Degrees of points on irreducible hypersurfaces

Lea Beneish, Andrew Granville

We study the set of $D$ such that a given irreducible hypersurface $C$ of degree $d$ has infinitely many points of degree $D$ over $Q$ . We give a new explicit proof that t…

math.NT2025

Fields generated by points on superelliptic curves

Lea Beneish, Christopher Keyes

We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $Q$ with fixed degree $n$ and discriminant b…

math.NT2024

How often does a cubic hypersurface have a rational point?

Lea Beneish, Christopher Keyes

A cubic hypersurface in $P^{n}$ defined over $Q$ is given by the vanishing locus of a cubic form $f$ in $n + 1$ variables. It is conjectured that when $n \geq 4$ , suc…

Effective Bertini theorems and zeros of p-adic forms of degrees 7 and 11

Degrees of points on irreducible hypersurfaces

Fields generated by points on superelliptic curves

How often does a cubic hypersurface have a rational point?

Effective Bertini theorems and zeros of $p$ -adic forms of degrees 7 and 11