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    <id>1759</id>
    <completedYear>2024</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2043</pageFirst>
    <pageLast>2074</pageLast>
    <pageNumber>32 Seiten</pageNumber>
    <edition/>
    <issue>2</issue>
    <volume>390</volume>
    <type>article</type>
    <publisherName>Springer Berlin Heidelberg</publisherName>
    <publisherPlace>Berlin/Heidelberg</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-01-29</completedDate>
    <publishedDate>2024-01-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Periods, power series, and integrated algebraic numbers</title>
    <abstract language="eng">Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the polynomial ring over the rationals and evaluate it at a rational number. We follow this path and close these algebraic power series under taking iterated antiderivatives and nearby algebraic and geometric operations. We obtain a system of rings of power series whose coefficients form a countable real closed field. Using techniques from o-minimality we are able to show that every period belongs to this field. In the setting of o-minimality we define exponential integrated algebraic numbers and show that exponential periods and the Euler constant is an exponential integrated algebraic number. Hence they are a good candiate for a natural number system extending the period ring and containing important mathematical constants.</abstract>
    <parentTitle language="eng">Mathematische Annalen</parentTitle>
    <identifier type="issn">0025-5831</identifier>
    <identifier type="issn">1432-1807</identifier>
    <identifier type="doi">10.1007/s00208-024-02802-2</identifier>
    <identifier type="urn">urn:nbn:de:101:1-2024040910285674698609</identifier>
    <enrichment key="opus.import.date">2025-07-29T13:03:19+00:00</enrichment>
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    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Tobias Kaiser</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>algebraic geometry</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>algebraic topology</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>algebra</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>associative rings and algebras</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>commutative rings and algebras</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>number theory</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Fakultät für Informatik und Mathematik</collection>
    <collection role="Import" number="import">Import</collection>
    <collection role="Transformationsvertrag" number="">DEAL Springer Nature</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/1759/00208_2024_Article_2802.pdf</file>
  </doc>
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