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

Let $K=\Bbb Q(\sqrt{-q})$, where $q$ is a prime congruent to $3$ modulo $4$.Let $A=A(q)$ denote the Gross curve. Let $E=A^{(-\beta)}$ denote its quadratictwist, with $\beta=\sqrt{-q}$. The curve $E$ is defined over the Hilbert classfield $H$ of $K$. We use Magma to calculate the values $L(E/H,1)$ for all such$q$'s up to some reasonable ranges (different for $q\equiv 7 \, \text{mod} \,8$ and $q\equiv 3 \, \text{mod} \, 8$). All these values are non-zero, andusing the Birch and Swinnerton-Dyer conjecture, we can calculate hypotheticalorders of $\sza(E/H)$ in these cases. Our calculations extend those given by J.Choi and J. Coates [{\it Iwasawa theory of quadratic twists of $X_0(49)$}, ActaMathematica Sinica(English Series) {\bf 34} (2017), 19-28] for the case $q=7$.

Critical $L$-values for some quadratic twists of Gross curves