Root number in non-isotrivial integer parameter families of elliptic curves
Desjardins, Julie
arXiv, 1810.12787 / Harvested from arXiv
Text on arXiv
In a previous article, the author proves that the value of the root number varies in a family of elliptic curves indexed by one parameter $t$ running through $\mathbb{Q}$. However, a well-known example of Washington has root number $-1$ for every fiber when $t$ runs through $\mathbb{Z}$. Such examples are rare since, as proven in this paper, the root number of the integer fibers varies for a large class of families of elliptic curves. Our results depends on the squarefree conjecture and Chowla's conjecture, and are unconditional in many cases.
Publié le : 2018-10-30
Classification:  Mathematics - Number Theory,  11G05, 11G40 
@article{1810.12787,
     author = {Desjardins, Julie},
     title = {Root number in non-isotrivial integer parameter families of elliptic
  curves},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.12787}
}

Desjardins, Julie. Root number in non-isotrivial integer parameter families of elliptic
  curves. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.12787/