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 study the distribution of the zeros of functions of the form $f(s)=h(s)\pm h(2a-s)$, where $h(s)$ is a meromorphic function, real on the real line,$a$ a real number. One of our results establishes sufficient conditions underwhich all but finitely many of the zeros of $f(s)$ lie on the line $\Re s = a$,called the {\it critical line} for the function $f(s)$, and be simple, giventhat all but finitely many of the zeros of $h(s)$ lie on the half-plane $\Re s< a$. This results can be regarded as a generalization of the necessarycondition of stability for the function $h(s)$, in the Hermite-Biehler theorem.We apply this results to the study of translations of the Riemann Zeta Functionand $L$ functions, and integrals of Eisenstein Series, among others.

Majoration du nombre de z\'eros d'une fonction m\'eromorphe en dehors d'une droite verticale et applications