Bibliographic Details
| Title: |
Shadow line distributions. |
| Authors: |
Balakrishnan, Jennifer S.1 (AUTHOR), Çiperiani, Mirela2 (AUTHOR), Mazur, Barry3 (AUTHOR), Rubin, Karl4 (AUTHOR) |
| Source: |
Mathematics of Computation. Sep2026, Vol. 95 Issue 361, p2539-2557. 19p. |
| Subjects: |
Elliptic curves, Quadratic fields, Hypothesis, Abelian groups |
| Abstract: |
Let E be an elliptic curve over \mathbb {Q} with Mordell–Weil rank 2 and p be an odd prime of good ordinary reduction. For every imaginary quadratic field K satisfying the Heegner hypothesis, there is (subject to the Shafarevich–Tate conjecture) a line, i.e., a free \mathbb {Z}_p-submodule of rank 1, in E(K)\otimes \mathbb {Z}_p given by universal norms coming from the Mordell–Weil groups of subfields of the anticyclotomic \mathbb {Z}_p-extension of K; we call it the shadow line. When the twist of E by K has analytic rank 1, the shadow line is conjectured to lie in E(\mathbb {Q})\otimes \mathbb {Z}_p; we verify this computationally in all our examples. We study the distribution of shadow lines in E(\mathbb {Q})\otimes \mathbb {Z}_p as K varies, framing conjectures based on the computations we have made. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
