Nuno Freitas

activity

20112026

most citedThe Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields

41 citations · 104 across the 25 of their papers we have counts for

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Showing 2020Show all

4 papers · 1 filter

math.NT2020★ 3 cited

On the unit equation over cyclic number fields of prime degree

Nuno Freitas, Alain Kraus, Samir Siksek

Let $ℓ \neq = 3$ be a prime. We show that there are only finitely many cyclic number fields $F$ of degree $ℓ$ for which the unit equation $$λ+ μ= 1, \qquad λ,~μ\in \mathcal{O}_F…

math.NT2020★ 7 cited

Local criteria for the unit equation and the asymptotic Fermat's Last Theorem

Nuno Freitas, Alain Kraus, Samir Siksek

Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat's Last Theorem to hold over F, and also for the non-existence o…

math.NT2020

Chevalley's class number formula, unit equations and the asymptotic Fermat's Last Theorem

Nuno Freitas, Alain Kraus, Samir Siksek

Let $F$ be a number field and $O_{F}$ its ring of integers. We use Chevalley's ambiguous class number formula to give a criterion for the non-existence of solutions to the…

math.NT2020★ 5 cited

On Asymptotic Fermat over $Z_{p}$ extensions of $Q$

Nuno Freitas, Alain Kraus, Samir Siksek

Let $p \geq 5$ be a prime and let $Q_{n, p}$ denote the $n$ -th layer of the cyclotomic $Z_{p}$ -extension of $Q$ . We show that $Q_{n, p}$ has no excep…

On the unit equation over cyclic number fields of prime degree

Local criteria for the unit equation and the asymptotic Fermat's Last Theorem

Chevalley's class number formula, unit equations and the asymptotic Fermat's Last Theorem

On Asymptotic Fermat over Zp​ extensions of Q

On Asymptotic Fermat over $Z_{p}$ extensions of $Q$