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 paper we construct the modular Cauchy kernel on the Hilbert modularsurface $\Xi_{\mathrm{Hil},m}(z)(z_2-\bar{z_2})$, i.e. the function of twovariables, $(z_1, z_2) \in \mathbb{H} \times \mathbb{H}$, which is invariantunder the action of the Hilbert modular group, with the first order pole on theHirzebruch-Zagier divisors. The derivative of this function with respect to$\bar{z_2}$ is the function $\omega_m (z_1, z_2)$ introduced by Don Zagier in\cite{Za1}. We consider the question of the convergence and the Fourierexpansion of the kernel function. The paper generalizes the first part of theresults obtained in the preprint \cite{Sa}

The modular Cauchy kernel for the Hilbert modular surface