Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Delaunay, Christophe"'
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case $m,n\leq2$.
Externí odkaz:
http://arxiv.org/abs/2109.00745
We study elliptic surfaces over $\mathbb{Q}(T)$ with coefficients of a Weierstrass model being polynomials in $\mathbb{Q}[T]$ with degree at most 2. We derive an explicit expression for their rank over $\mathbb{Q}(T)$ depending on the factorization a
Externí odkaz:
http://arxiv.org/abs/2109.00738
We consider the problem of finding $1$-parameter families of elliptic curves whose root number does not average to zero as the parameter varies in $\mathbb{Z}$. We classify all such families when the degree of the coefficients (in the parameter $t$)
Externí odkaz:
http://arxiv.org/abs/1612.03095
Autor:
Delaunay, Christophe, Jouhet, Frédéric
This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to E.
Externí odkaz:
http://arxiv.org/abs/1303.7337
Autor:
Delaunay, Christophe, Jouhet, Frédéric
The main aim of this article is to compute all the moments of the number of $p^\ell$-torsion elements in some type of nite abelian groups. The averages involved in these moments are those de ned for the Cohen-Lenstra heuristics for class groups and t
Externí odkaz:
http://arxiv.org/abs/1208.6397
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some technical conditi
Externí odkaz:
http://arxiv.org/abs/1112.0166
Publikováno v:
Transactions of the American Mathematical Society 365, 6 (2013) 3227-3253
In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Ro
Externí odkaz:
http://arxiv.org/abs/1101.1199
We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators. We also describe an efficient algorithm
Externí odkaz:
http://arxiv.org/abs/0707.0772
Publikováno v:
In Journal of Number Theory October 2018 191:1-84
Autor:
Delaunay, Christophe, Jouhet, Frédéric
Publikováno v:
In Advances in Mathematics 20 June 2014 258:13-45