English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $p$ be a prime number and let $ k $ be a number field, which does notcontain the field $\mathbb{Q} (\zeta_p + \bar{\zeta_p})$. Let $\mathcal{E}$ bean elliptic curve defined over $k$. We prove that if there are no $k$-rationaltorsion points of exact order $p$ on $\E$, then the local-global principleholds for divisibility by $p^n$, with $n$ a natural number. As a consequence ofthe deep theorem of Merel, for $p$ larger than a constant depending only on thedegree of $k$, there are no counterexamples to the local-global divisibilityprinciple. Nice and deep works give explicit small constants for ellipticcurves defined over a number field of degree at most 5 over $\mathbb{Q}.

On local-global divisibility by $p^n$ in elliptic curves