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/

Zendy Plus

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

Zendy Tools

Zendy Open

Based on an equation for the rank of an elliptic surface over $\mathbb{Q}$which appears in the work of Nagao, Rosen, and Silverman, we conjecture that100% of elliptic surfaces have rank $0$ when ordered by the size of thecoefficients of their Weierstrass equations, and present a probabilisticheuristic to justify this conjecture. We then discuss how it would follow fromeither understanding of certain $L$-functions, or from understanding of thelocal behaviour of the surfaces. Finally, we make a conjecture about ranks ofelliptic surfaces over finite fields, and highlight some experimental evidencesupporting it.

Conjecture: 100% of elliptic surfaces over $\mathbb{Q}$ have rank zero