Andrew O'Desky

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math.NT2024

Integral points on singular toric varieties and cyclic normal polynomials

Andrew O'Desky

We establish a formula for the height zeta function for integral points on a class of projective toric varieties. Our method builds on the harmonic analysis approach of Batyrev--Ts…

math.NT2024

On trace-one generators of abelian cubic fields

Andrew O'Desky

Let $K$ be a tamely ramified abelian cubic number field with discriminant $D_{K}$ . We prove that the number of trace-one monic integral polynomials with root field $K$ and height $H$ …

math.NT2023

On monic abelian trace-one cubic polynomials

Shubhrajit Bhattacharya, Andrew O'Desky

We compute the asymptotic number of monic trace-one integral polynomials with Galois group $C_{3}$ and bounded height. For such polynomials we compute a height function coming from t…