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

We compute an asymptotic formula for the divisor class numbers of  real  cubic function fieldsKm=k(m3){K}_{m}=k\left(\sqrt[3]{m}), whereFq{{\mathbb{F}}}_{q}is a finite field withqqelements,q≡1(mod3)q\equiv 1\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3),k≔Fq(T)k:= {{\mathbb{F}}}_{q}\left(T)is the rational function field, andm∈Fq[T]m\in {{\mathbb{F}}}_{q}\left[T]is a cube-free polynomial; in this case, the degree ofmmis divisible by 3. For computation of our asymptotic formula, we find the average value of∣L(s,χ)∣2{| L\left(s,\chi )| }^{2}evaluated ats=1s=1whenχ\chigoes through the primitive cubic  even  Dirichlet characters ofFq[T]{{\mathbb{F}}}_{q}\left[T], whereL(s,χ)L\left(s,\chi )is the associated DirichletLL-function.

Average value of the divisor class numbers of real cubic function fields