Munshi, Ritabrata (2007) Density of positive rank fibers in elliptic fibrations Journal of Number Theory, 125 (1). pp. 254-266. ISSN 0022-314X
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Official URL: http://www.sciencedirect.com/science/article/pii/S...
Related URL: http://dx.doi.org/10.1016/j.jnt.2006.10.019
Abstract
A question of Mazur asks whether for any non-constant elliptic fibration {Er}r∈ℚ, the set {r∈ℚ: rank(Er(ℚ))>0}, if infinite, is dense in ℝ (with respect to the Euclidean topology). This has been proved to be true for the family of quadratic twists of a fixed elliptic curve by a quadratic or a cubic polynomial. Here we settle Mazur's question affirmatively for the general quadratic and cubic fibrations. Moreover we show that our method works when is ℚ replaced by any real number field.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Elliptic Pencil; Rational Points |
| ID Code: | 110848 |
| Deposited On: | 31 Jan 2018 09:09 |
| Last Modified: | 31 Jan 2018 09:09 |
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