Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On rational approximation of algebraic functions
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
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]

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

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

Open Access in DiVA

fulltext(356 kB)41 downloads
File information
File name FULLTEXT01.pdfFile size 356 kBChecksum SHA-512
61e855ee326ce471cdb6f82f92ca3f6c93490a66f2d9f973668a2d0e892aea1259fe203109549c5f8f0d0dcfb767096a84338e41910b6cf05b42bfecb2ef71f1
Type fulltextMimetype application/pdf

Other links

Publisher's full texthttp://www.math.su.se/~shapiro

Search in DiVA

By author/editor
Shapiro, Boris
By organisation
Department of Mathematics
In the same journal
Advances in Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 41 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 58 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf