P. Koymans

activity

20162026

16

-rank of class groups of

Q (- 2 p)

for primes

p \equiv 1 mod 4

11 citations · 57 across the 34 of their papers we have counts for

collaborators

Showing 2025Show all

5 papers · 1 filter

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

Asymptotics for $6$ -torsion and $D_{6}$ -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 $6$ -torsion of the class group of quadratic number field…

math.NT2025

Constructing Jacobians of rank 1

Peter Koymans, Adam Morgan

Let $K$ be a number field, let $g \geq 1$ be an integer and let $f (x) = (x - a_{1}) \dots (x - a_{2 g + 1}) \in O_{K} [x]$ be a polynomial that splits into $2 g + 1$ distinct linear fact…

math.NT2025

Elliptic curves of rank one over number fields

Peter Koymans, Carlo Pagano

We prove that for every number field $K$ , there exist infinitely many elliptic curves $E$ over $K$ with rank exactly equal to 1.

math.NT2025

A new pointwise bound for $3$ -torsion of class groups

Stephanie Chan, Peter Koymans

Ellenberg--Venkatesh proved in 2007 that $h_{3} (d) ≪_{ε} ∣ d ∣^{1/3 + ε}$ , where $h_{3} (d)$ denotes the size of the $3$ -torsion of the class group of $Q (d)$ . We improve th…

Statistics of bad parts of class groups

Asymptotics for 6-torsion and D6​-extensions

Constructing Jacobians of rank 1

Elliptic curves of rank one over number fields

A new pointwise bound for 3-torsion of class groups

Asymptotics for $6$ -torsion and $D_{6}$ -extensions

A new pointwise bound for $3$ -torsion of class groups