Carlo Pagano

activity

20162026

Cl (K) [l^{\infty}]

for degree

l

cyclic fields

6 citations · 33 across the 23 of their papers we have counts for

collaborators

Showing 2024Show all

5 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

Diophantine stability and second order terms

Carlo Pagano, Efthymios Sofos

We establish a Galois-theoretic trichotomy governing Diophantine stability for genus $0$ curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine s…

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

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

Diophantine stability and second order terms

Elliptic fibrations and 3⋅2k

Averages of multiplicative functions along equidistributed sequences

6-torsion and integral points on quartic threefolds

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

$6$ -torsion and integral points on quartic threefolds