5 papers · 1 filter
The strong form of Van der Waerden's conjecture via twisted Chowla
Theresa C. Anderson, Sam Chow, Rainer Dietmann +3
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…
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…
Generalised Fermat equations in dense variables over finite fields and rings
Sam Chow, Zi Li Lim, Akshat Mudgal
Let be a sufficiently dense subset of a finite field or a finite, cyclic ring . Assuming that and have no small prime divisors, we…
Twisted Diophantine approximation for matrix transformations of tori
Sam Chow, Qing-Long Zhou
Consider a sequence of integral matrices , and a -tuple function . For a fixed vector ${\bm α}…
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…