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math.NT2026
The Artin-Davenport conjecture on cubic forms
Dante Bonolis, Tim Browning, Jakob Glas +1
We show that any integral cubic form in ten or more variables has a nontrivial integer zero. Like earlier authors on this topic, we use geometric methods to produce a zero in some…
math.NT2026
Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization
Dante Bonolis, Lillian B. Pierce, Katharine Woo
We develop the theory of strongly -genuine polynomials , which have the property that the number of specializations with $\mathbf{x}'…
math.NT2026
Counting points in thin sets: A survey
Dante Bonolis, Lillian B. Pierce, Katharine Woo
In the 1980's Serre asked how many points of bounded height can lie in a thin set. This has motivated significant research ever since, culminating in a series of recent breakthroug…