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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let us consider $\mathbb{K}$ be a complete ultrametric algebraically closed field and suppose $\mathcal{A}\left( \mathbb{K}\right) $ be the $\mathbb{K}$-algebra of entire functions on $\mathbb{K}$. For any $p$-adic entire functions $f\in\mathcal{A}\left( \mathbb{K}\right) $ and $r>0$, we denote by $|f|\left(r\right)$ the number $\sup \left\{ |f\left( x\right) |:|x|=r\right\},$ where $\left\vert \cdot \right\vert (r)$ is a multiplicative norm on $\mathcal{A}\left(\mathbb{K}\right).$ For another $p$-adic entire functions $g\in\mathcal{A}\left( \mathbb{K}\right),$ $|g|\left(r\right) $ is defined and the ratio $\frac{|f|\left( r\right) }{|g|\left( r\right) }$ as $r\rightarrow \infty $ is called the comparative growth of $f$ with respect to $g$ in terms of their multiplicative norm. Likewise to complex analysis, in this paper we define the concept of $(p,q)$th order (respectively $(p,q)$th lower order) of growth as $\rho^{\left(p,q\right)} \left( f\right) =\underset{r\rightarrow +\infty }{\lim \sup} \frac{\log ^{[p]}|f| \left(r\right) }{\log ^{\left[ q\right] }r}$ (respectively $\lambda ^{\left( p,q\right) } \left(f\right) =\underset{r\rightarrow +\infty }{\lim\inf }\frac{\log ^{[p]}|f|\left( r\right)} {\log^{\left[ q\right] }r}$), where $p$ and $q$ are any two positive integers. We study then some growth properties of composite $p$-adic entire functions on the basis of their $\left( p,q\right)$th order and $(p,q)$th lower order where $p$ and $q$ are any two positive integers.

$(p,q)$th order oriented growth measurement of composite $p$-adic entire functions