Reference : Effective Kummer Theory for Elliptic Curves
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/43271
Effective Kummer Theory for Elliptic Curves
English
Lombardo, Davide mailto [Università di Pisa > Dipartimento di Matematica]
Tronto, Sebastiano mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Undated
No
[en] Elliptic curves ; Kummer Theory
[en] Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite
order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective
and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])].
When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality
[Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α.
http://hdl.handle.net/10993/43271
https://arxiv.org/abs/1909.05376

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
explicit_open_image.pdfAuthor preprint482.87 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.