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pro vyhledávání: '"Nicolas Mascot"'
Autor:
Nicolas Mascot, Denis Simon
Publikováno v:
Expositiones Mathematicae.
We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7e5ce7a682c514dfb8bb5f8ca96d313
https://doi.org/10.1016/j.exmath.2023.02.006
https://doi.org/10.1016/j.exmath.2023.02.006
Autor:
Nicolas Mascot
Publikováno v:
Foundations of Computational Mathematics. 23:519-543
We describe a method to compute mod $$\ell $$ ℓ Galois representations contained in the $${{\text {H}}}_{\acute{\mathrm{e}}\mathrm{t}}^2$$ H e ´ t 2 of surfaces. We apply this method to the case of a representation with values in $${\text {GL}}_3(
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ad098333fd69bf058ccebd32f039000c
https://doi.org/10.1007/s10208-021-09505-z
https://doi.org/10.1007/s10208-021-09505-z
Autor:
Nicolas Mascot
Publikováno v:
Mathematics of Computation. 89:1417-1455
Let $\rho$ be a mod $\ell$ Galois representation. We show how to compute $\rho$, given the characteristic polynomial of the image of the Frobenius at one prime $p$ and a curve $C$ whose Jacobian contains $\rho$ in its $\ell$-torsion. The main ingredi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0733ee012c9ceceb6ea659db2d4466af
https://doi.org/10.1090/mcom/3484
https://doi.org/10.1090/mcom/3484
Publikováno v:
Arithmetic Geometry, Number Theory, and Computation ISBN: 9783030809133
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::21b5b60bc2cf8984af40dd4aaebf41a5
https://doi.org/10.1007/978-3-030-80914-0_20
https://doi.org/10.1007/978-3-030-80914-0_20
Autor:
Nicolas Mascot
We show how our p-adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is the use of "moduli-friendly" Eisenstein series introduced by Makdisi, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::765bcf80ebadb5e81bdbf663c0c6b8ce
We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.
37 pages, 1 figure; v5 missing reference added
37 pages, 1 figure; v5 missing reference added
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3ac20fc351471821e20ac8982cbfb9b3
http://arxiv.org/abs/1705.09248
http://arxiv.org/abs/1705.09248
Autor:
Nicolas Mascot
In previous works, we described algorithms to compute the number field cut out by the mod ell representation attached to a modular form of level N=1. In this article, we explain how these algorithms can be generalised to forms of higher level N. As a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::922c66995e3a2628743a26d99182bd47
http://arxiv.org/abs/1611.01464
http://arxiv.org/abs/1611.01464
Autor:
Nicolas Mascot
Publikováno v:
Rendiconti del Circolo Matematico di Palermo
Rendiconti del Circolo Matematico di Palermo, 2013, 62 (3), pp.451-476. ⟨10.1007/s12215-013-0136-4⟩
Rendiconti del Circolo Matematico di Palermo, 2013, 62 (3), pp.451-476. ⟨10.1007/s12215-013-0136-4⟩
We compute modular Galois representations associated with a newform $f$, and study the related problem of computing the coefficients of $f$ modulo a small prime $\ell$. To this end, we design a practical variant of the complex approximations method p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c321073d883c67a7c9ed02a7a3d12ce
http://hdl.handle.net/20.500.12278/114216
http://hdl.handle.net/20.500.12278/114216
Autor:
Nicolas Mascot
We show how the output of the algorithm to compute modular Galois representations described in our previous article can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an improved
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb083025a14bd0ffc3658240ea37b745