Author

Peter Koymans

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Preprint Aug 2026

The strong form of Van der Waerden's conjecture via twisted Chowla

Determining the properties of a random polynomial has fuelled significant investigation over the past century. One driving force of this research is a 1936 paper of Van der Waerden. Fix $n \ge 3$ and let $E_n(B)$ be the number of monic, irreducible, non-$S_n$ polynomials $f = X^n + a_1 X^{n-1} + \cdots + a_n$ with $|a_...

Theresa C. Anderson, Sam Chow, R. Dietmann et al. · 1 citation

Preprint Sep 2026

Chowla's non-vanishing conjecture over $\mathbb{F}_q(T)$

Let $q \equiv 1 \bmod 8$ be a prime power. We prove that $L\left(\tfrac{1}{2}, \chi\right) \neq 0$ for 100% of the imaginary quadratic Dirichlet characters of $\mathbb{F}_q(T)$.

Peter Koymans, Carlo Pagano, M. Shusterman · 0 citations

Preprint Aug 2026

The strong form of Van der Waerden's conjecture via twisted Chowla

Determining the properties of a random polynomial has fuelled significant investigation over the past century. One driving force of this research is a 1936 paper of Van der Waerden. Fix $n \geq 3$ and let $E_n(B)$ be the number of monic, irreducible, non-$S_n$ polynomials $f = X^n + a_1 X^{n-1} + \cdots + a_n$ with $|a...

Theresa C. Anderson, Sam Chow, R. Dietmann et al. · 0 citations