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 zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

An algebraic function of the third order plays an important role in theproblem of asymptotics of Hermite-Pad\'e approximants for two analyticfunctions with branch points. This algebraic function appears as the Cauchytransform of the limiting measure of the asymptotic distribution of the polesof the approximants. In many cases this algebraic function can be determined byusing the given position of the branch points of the functions which areapproximated and by the condition that its Abelian integral has purelyimaginary periods. In the present paper we obtain a hyperellipticuniformization of this algebraic function. In the case when each approximatedfunction has only two branch points, the genus of this function can be equal to0, 1 (elliptic case) or 2 (ultra-elliptic case). We use this uniformization toparametrize the elliptic case. This parametrization allows us to obtain anumerical procedure for finding this elliptic curve and as a result we candescribe the limiting measure of the distribution of the poles of theapproximants.

Hyperelliptic uniformization of algebraic curves of the third order