11 citations · 57 across the 34 of their papers we have counts for
40 papers
Chowla's non-vanishing conjecture over
Peter Koymans, Carlo Pagano, Mark Shusterman
Let be a prime power. We prove that for 100% of the imaginary quadratic Dirichlet characters of .
The strong form of Van der Waerden's conjecture via twisted Chowla
Theresa C. Anderson, Sam Chow, Rainer Dietmann +5
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…
Tamagawa ratios and unbounded Selmer moments
Peter Koymans, Alexander Smith
We develop a framework to predict whether a family of Selmer groups has average size that is bounded or unbounded. Applying this framework to certain geometric families of abelian…
Hilbert's tenth problem for finitely generated rings
Peter Koymans, Carlo Pagano
This expository article covers the recent developments surrounding Hilbert's tenth problem for finitely generated rings. We start by recounting the history of Hilbert's tenth probl…
Statistics of bad parts of class groups
Peter Koymans, Yuan Liu
Let be an odd prime. We give a formula for the bad part of -class groups that is valid for of the abelian -extensions when ordered by product of ramified primes.
Asymptotics for -torsion and -extensions
Peter Koymans, Robert J. Lemke Oliver, Efthymios Sofos +1
We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average -torsion of the class group of quadratic number field…