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On rational approximation of algebraic functionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2006 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 204, no 2, 448-480 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2006. Vol. 204, no 2, 448-480 p.
##### Keyword [en]

finite recursions; asymptotic ratio distribution; Pade approximation
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-20604DOI: 10.1016/j.aim.2005.06.002OAI: oai:DiVA.org:su-20604DiVA: diva2:187130
#####

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Available from: 2010-12-31 Created: 2007-11-28 Last updated: 2017-12-13Bibliographically approved

We construct a new scheme of approximation of any multivalued algebraic function f (z) by a sequence {r(n)(z)}(n is an element of N) of rational functions. The latter sequence is generated by a recurrence relation which is completely determined by the algebraic equation satisfied by f(z). Compared to the usual Pade approximation our scheme has a number of advantages, such as simple computational procedures that allow us to prove natural analogs of the Pade Conjecture and Nuttall's Conjecture for the sequence {r(n)(z)}(n is an element of N) in the complement CP1\D-f, where D-f is the union of a finite number of segments of real algebraic curves and finitely many isolated points. In particular, our construction makes it possible to control the behavior of spurious poles and to describe the asymptotic ratio distribution of the family {r(n)(z)}(n is an element of N). As an application we settle the so-called 3-conjecture of Egecioglu et al. dealing with a 4-term recursion related to a polynomial Riemann Hypothesis

doi
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