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- W2965937315 abstract "We fix $z_0inmathbb C$ and a field $mathbb F$ with $mathbb Csubset mathbb F subset mathcal M_{z_0}:=$ the field of germs of meromorphic functions at $z_0$. We fix $f_1,ldots,f_rin mathcal M_{z_0}$ and we consider the $mathbb F$-algebras $S:=mathbb F[f_1,ldots,f_r]$ and $overline S:=mathbb F[f_1^{pm 1},ldots,f_r^{pm 1}]$. We present the general properties of the semigroup rings begin{align*} & S^{hol}:=mathbb F[f^{mathbf a}:=f_1^{a_1}cdots f_r^{a_r}: (a_1,ldots,a_r)inmathbb N^r text{ and }f^{mathbf a}text{ is holomorphic at & overline S^{hol}:=mathbb F[f^{mathbf a}:=f_1^{a_1}cdots f_r^{a_r}: (a_1,ldots,a_r)inmathbb Z^r text{ and }f^{mathbf a}text{ is holomorphic at }z_0], end{align*} and we tackle in detail the case in which $mathbb F=mathcal M_{<1}$ is the field of meromorphic functions of order $<1$ and $f_j$'s are meromorphic functions over $mathbb C$ of finite order with a finite number of zeros and poles." @default.
- W2965937315 created "2019-08-13" @default.
- W2965937315 creator A5032965447 @default.
- W2965937315 date "2019-07-28" @default.
- W2965937315 modified "2023-09-27" @default.
- W2965937315 title "Two semigroup rings associated to a finite set of germs of meromorphic functions" @default.
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