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Uniqueness for p-adic meromorphic products
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik. (Matematisk modellering)ORCID iD: 0000-0002-7825-4428
2006 (English)In: Mathematical ReviewsArticle, book review (Other (popular science, discussion, etc.)) Published
Abstract [en]

MR2232636

Boussaf, Kamal(F-CLEF2-LPM)

Uniqueness for $p$-adic meromorphic products. (English summary)

Bull. Belg. Math. Soc. Simon Stevin 9 (2002), suppl., 11--23.

32P05 (32H04)

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In the paper under review the author looks for bi-unique range sets (bi-urs) for the family of unbounded meromorphic products on an open disk. More precisely, let $K$ be a complete ultrametric algebraically closed field of characteristic zero, and let $\scr{M}(K)$ be the field of meromorphic functions in $K$. Denote by $\scr{MP}_{u}(K,R)$ the subset of meromorphic products admitting an irreducible form $\prod_{n=0}^{\infty}\frac{x-a_n}{x-b_n}$ such that $\prod_{n=0, b_n\neq 0}^{\infty}\frac{|b_n|}{R}=0$. The main result in the paper under review implies that for every $n\geq5$, there exist sets $S$ of $n$ elements in $K$ such that $(S,\{\infty\})$ is a bi-urs for $\scr{MP}_u(K,R)$.

Earlier, A. Boutabaa and A. Escassut proved that for every $n\geq5$, there exist sets $S$ of $n$ elements in $K$ such that $(S,\{w\})$ is a bi-urs for $\scr{M}(K)$. H. H. Khoi and T. T. H. An showed the existence of bi-urs for $\scr{M}(K)$ of the form $(\{a_1,a_2,a_3,a_4\},\{\infty\})$.

Reviewed by Karl-Olof Lindahl

Place, publisher, year, edition, pages
2006.
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-4442OAI: oai:DiVA.org:vxu-4442DiVA, id: diva2:204400
Note
15 December 2006 Review för American Mathematical Society i serien Mathematical Reviews on the Web av artikeln Bekräftas med följande e-post X-Sieve: CMU Sieve 2.2 Date: Fri, 15 Dec 2006 00:17:41 -0500 From: mathrev@ams.org Subject: Review received (MR2232636) To: karl-olof.lindahl@vxu.se X-VXU-MailScanner-Information: Please contact the ISP for more information X-VXU-MailScanner: Found to be clean X-VXU-MailScanner-SpamCheck: not spam, SpamAssassin (not cached, score=-1.638, required 5, BAYES_00 -2.60, NO_REAL_NAME 0.96) X-VXU-MailScanner-From: webrev@ams.org http://www.ams.org/mathscinet/pdf/2232636.pdf?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&s4=boussaf&s5=&s6=&s7=&s8=All&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=3Available from: 2007-03-30 Created: 2007-03-30 Last updated: 2014-02-20Bibliographically approved

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