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Non-isotrivial elliptic surfaces with non-zero average root number

Title:

Non-isotrivial elliptic surfaces with non-zero average root number

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:26 Apr 2018 20:02

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