Yuan Liu

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20232025

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math.NT2025

Statistics of bad parts of class groups

Peter Koymans, Yuan Liu

Let $p$ be an odd prime. We give a formula for the bad part of $p$ -class groups that is valid for $100%$ of the abelian $p$ -extensions when ordered by product of ramified primes.

math.NT2025

The imaginary case of the nonabelian Cohen--Lenstra heuristics

Yuan Liu, Ken Willyard

For a finite group $Γ$ , we study the distribution of the Galois group $G_{\emptyset}^{#} (K)$ of the maximal unramified extension of $K$ that is split completely at $\infty$ and ha…

math.NT2024

On the Distribution of Class Groups of Abelian Extensions

Yuan Liu

Given a finite abelian group $Γ$ , we study the distribution of the $p$ -part of the class group $Cl (K)$ as $K$ varies over Galois extensions of $Q$ or $\math…