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

In this work we consider constructions of genus three curves $X$ such that$\mathrm{End}(\mathrm{Jac}(X)) \otimes Q$ contains the totally real cubicnumber field $Q(\zeta _ 7 + \overline{\zeta}_7)$. We construct explicittwo-dimensional families defined over $Q(s; t)$ whose generic member is anonhyperelliptic genus 3 curve with this property. The case when X ishyperelliptic was studied by the authors Hoffman and Wang in a previous work.We calculate the zeta function of one of these curves. Conjecturally this zetafunction is described by a modular form.

Genus 3 curves whose Jacobians have endomorphisms by $Q(\zeta _7 + \overline{\zeta}_7)$