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pro vyhledávání: '"Dieulefait, Luis"'
Autor:
Dieulefait, Luis Víctor, Urróz, Jorge
In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. The algorithm consists only on a computation of a greatest common divisor, two multiplic
Externí odkaz:
http://arxiv.org/abs/2406.04061
Autor:
Blanco-Chacón, Iván, Dieulefait, Luis
Let $F/\mathbb{Q}$ be any totally real number field and $\frak{N}$ an ideal of its ring of integers of norm $N$ and define, for every even $n$, the $[F:\mathbb{Q}]$-dimensional multiweight $\textbf{n}=(n,...,n)$. We prove that for a non CM Hilbert cu
Externí odkaz:
http://arxiv.org/abs/2310.11522
In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of $\mathrm{GL}_2$-type over totally real fields. The original approach was based on hard open conjectures, which have made it difficul
Externí odkaz:
http://arxiv.org/abs/2205.15861
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the previous o
Externí odkaz:
http://arxiv.org/abs/2108.07577
Autor:
Blanco-Chacón, Iván, Dieulefait, Luis
We prove that for a Hecke cuspform $f\in S_k(\Gamma_0(N),\chi)$ and a prime $l>\max\{k,6\}$ such that $l\nmid N$, there exists an infinite family $\{k_r\}_{r\geq 1}\subseteq\mathbb{Z}$ such that for each $k_r$, there is a cusp form $f_{k_r}\in S_{k_r
Externí odkaz:
http://arxiv.org/abs/2008.04192
Akademický článek
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Autor:
Dieulefait, Luis, Urroz, Jorge
In this paper we address two different problems related with the factorization of an RSA module N. First we can show that factoring is equivalent in deterministic polynomial time to counting points on a pair of twisted Elliptic curves modulo N. Also
Externí odkaz:
http://arxiv.org/abs/1911.11004
Autor:
Dieulefait, Luis, Soto, Eduardo
In this paper we prove new cases of the asymptotic Fermat equation with coefficients. This is done by solving remarkable $S$-units equations and applying a method of Frey-Mazur.
Externí odkaz:
http://arxiv.org/abs/1811.05957
Autor:
Dieulefait, Luis, Soto, Eduardo
In this paper we prove a level raising theorem for some weight $2$ trivial character newforms at almost every prime $p$. This is done by ignoring the residue characteristic at which the level raising appears.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/1805.10937
Counting the number of Galois orbits of newforms in $S_k(\Gamma_0(N))$ and giving some arithmetic sense to this number is an interesting open problem. The case $N=1$ corresponds to Maeda's conjecture (still an open problem) and the expected number of
Externí odkaz:
http://arxiv.org/abs/1805.10361