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 2024Show all

9 papers · 1 filter

math.NT2024

Hilbert's tenth problem via additive combinatorics

Peter Koymans, Carlo Pagano

For all infinite rings $R$ that are finitely generated over $Z$ , we show that Hilbert's tenth problem has a negative answer. This is accomplished by constructing elliptic…

math.NT2024

Elliptic fibrations and $3 \cdot 2^{k}$

Peter Koymans, Carlo Pagano, Efthymios Sofos

We determine the order of magnitude for all exponential moments of the rank in a broad class of elliptic fibrations and for the $3 \cdot 2^{k}$ -torsion in the class group of quadrati…

math.NT2024

Sums of rational cubes and the $3$ -Selmer group

Peter Koymans, Alexander Smith

Recently, Alpöge-Bhargava-Shnidman determined the average size of the $2$ -Selmer group in the cubic twist family of any elliptic curve over $Q$ with $j$ -invariant $0$ . We…

math.NT2024

Binary forms with the same value set III. The case of $D_{3}$ and $D_{6}$

Étienne Fouvry, Peter Koymans

Let $F, G \in Z [X, Y]$ be binary forms of degree $\geq 3$ with automorphism groups isomorphic to the dihedral group of cardinality $6$ or $12$ . We characterize exactly whe…

math.NT2024

Binary quadratic forms with the same value set

Étienne Fouvry, Peter Koymans

Given a binary quadratic form $F \in Z [X, Y]$ , we define its value set $F (Z^{2})$ to be ${F (x, y) : (x, y) \in Z^{2}}$ . If $F$ and $G$ are two binary quadr…

math.NT2024

Binary forms with the same value set II. The case of $D_{4}$

Étienne Fouvry, Peter Koymans

Let $F, G \in Z [X, Y]$ be binary forms of degree $\geq 3$ , non-zero discriminant and with automorphism group isomorphic to $D_{4}$ . If $F (Z^{2}) = G (Z^{2})$ , w…

math.NT2024★ 1 cited

Binary forms with the same value set I

Étienne Fouvry, Peter Koymans

Given a binary form $F \in Z [X, Y]$ , we define its value set to be ${F (x, y) : (x, y) \in Z^{2}}$ . Let $F, G \in Z [X, Y]$ be two binary forms of degree $…

math.NT2024

Averages of multiplicative functions along equidistributed sequences

Stephanie Chan, Peter Koymans, Carlo Pagano +1

For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.

math.NT2024★ 1 cited

$6$ -torsion and integral points on quartic threefolds

Stephanie Chan, Peter Koymans, Carlo Pagano +1

We prove matching upper and lower bounds for the average of the 6-torsion of class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine qu…

Hilbert's tenth problem via additive combinatorics

Elliptic fibrations and 3⋅2k

Sums of rational cubes and the 3-Selmer group

Binary forms with the same value set III. The case of D3​ and D6​

Binary quadratic forms with the same value set

Binary forms with the same value set II. The case of D4​

Binary forms with the same value set I

Averages of multiplicative functions along equidistributed sequences

6-torsion and integral points on quartic threefolds

Elliptic fibrations and $3 \cdot 2^{k}$

Sums of rational cubes and the $3$ -Selmer group

Binary forms with the same value set III. The case of $D_{3}$ and $D_{6}$

Binary forms with the same value set II. The case of $D_{4}$

$6$ -torsion and integral points on quartic threefolds