Sam Chow

collaborators

4 papers

math.NT2026

Enumerative Galois theory for number fields

Sam Chow, Rainer Dietmann

Counting number fields with prescribed Galois group is an enduring challenge in arithmetic statistics. Using the determinant method, we provide an upper bound for even groups, whic…

math.NT2025

Generalised Fermat equations in dense variables over finite fields and rings

Sam Chow, Zi Li Lim, Akshat Mudgal

Let $A$ be a sufficiently dense subset of a finite field $F_{q}$ or a finite, cyclic ring $Z / N Z$ . Assuming that $q$ and $N$ have no small prime divisors, we…

math.NT2025

Twisted Diophantine approximation for matrix transformations of tori

Sam Chow, Qing-Long Zhou

Consider a sequence of integral matrices $A = (A_{n})_{n \in N}$ , and a $d$ -tuple function $r = (r_{1}, \dots, r_{d}) : N \to (0, \frac{1}{2})$ . For a fixed vector ${\bm Î±}…

math.NT2025

General Duffin--Schaeffer-type counterexamples in diophantine approximation

Sam Chow, Manuel Hauke, Andrew Pollington +1

Duffin and Schaeffer provided a famous counterexample to show that Khintchine's theorem fails without monotonicity assumption. Given any monotonically decreasing approximation func…