Bettin, Sandro, David, Chantal and Delaunay, Christophe (2018) Non-isotrivial elliptic surfaces with non-zero average root number. Journal of Number Theory . ISSN 0022314X (In Press)
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Official URL: http://dx.doi.org/10.1016/j.jnt.2018.03.007
Abstract
We consider the problem of finding non-isotrivial 1-parameter families of elliptic curves whose root number does not average to zero as the parameter varies in Z. We classify all such families when the degree of the coefficients (in the parameter t ) is less than or equal to 2 and we compute the rank over Q(t) of all these families. Also, we compute explicitly the average of the root numbers for some of these families highlighting some special cases. Finally, we prove some results on the possible values average root numbers can take, showing for example that all rational number in [−1,1] are average root numbers for some non-isotrivial 1-parameter family
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Article |
| Refereed: | Yes |
| Authors: | Bettin, Sandro and David, Chantal and Delaunay, Christophe |
| Journal or Publication: | Journal of Number Theory |
| Date: | 17 April 2018 |
| Digital Object Identifier (DOI): | 10.1016/j.jnt.2018.03.007 |
| Keywords: | Rational elliptic surface; Rank; Root number; Average root number |
| ID Code: | 983801 |
| Deposited By: | ALINE SOREL |
| Deposited On: | 26 Apr 2018 20:01 |
| Last Modified: | 17 Apr 2020 00:00 |
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