<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04458844</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-15T05:03:02+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The extended Eulerian numbers over function fields</title>
            <author role="crp">
              <persName>
                <forename type="first">Abdelmejid</forename>
                <surname>Bayad</surname>
              </persName>
              <email type="md5">47b1a05659d86036d732b65eb30913b1</email>
              <email type="domain">univ-evry.fr</email>
              <idno type="idhal" notation="numeric">1251167</idno>
              <idno type="halauthorid" notation="string">2800414-1251167</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8003-335X</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-0867-8305</idno>
              <idno type="IDREF">https://www.idref.fr/06885871X</idno>
              <idno type="VIAF">https://viaf.org/viaf/200933408</idno>
              <idno type="ISNI">http://isni.org/isni/0000000431595166</idno>
              <affiliation ref="#struct-419361"/>
              <affiliation ref="#struct-1002387"/>
              <affiliation ref="#struct-300306"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Mounir</forename>
                <surname>Hajli</surname>
              </persName>
              <idno type="halauthorid">2014829-0</idno>
              <affiliation ref="#struct-1059435"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Abdelmejid</forename>
                <surname>BAYAD</surname>
              </persName>
              <email type="md5">47b1a05659d86036d732b65eb30913b1</email>
              <email type="domain">univ-evry.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-02-15 08:49:15</date>
              <date type="whenModified">2025-04-17 10:12:05</date>
              <date type="whenReleased">2024-02-15 08:49:15</date>
              <date type="whenProduced">2022</date>
              <ref type="externalLink" target="http://www.doiserbia.nb.rs/ft.aspx?id=1452-86302200019B"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1331004">
                <persName>
                  <forename>Abdelmejid</forename>
                  <surname>BAYAD</surname>
                </persName>
                <email type="md5">47b1a05659d86036d732b65eb30913b1</email>
                <email type="domain">univ-evry.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04458844</idno>
            <idno type="halUri">https://hal.science/hal-04458844</idno>
            <idno type="halBibtex">bayad:hal-04458844</idno>
            <idno type="halRefHtml">&lt;i&gt;Applicable Analysis and Discrete Mathematics&lt;/i&gt;, 2022, 16 (2), pp.508-523. &lt;a target="_blank" href="https://dx.doi.org/10.2298/AADM210930019B"&gt;&amp;#x27E8;10.2298/AADM210930019B&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Applicable Analysis and Discrete Mathematics, 2022, 16 (2), pp.508-523. &amp;#x27E8;10.2298/AADM210930019B&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-EVRY">Université d'Evry-Val d'Essonne</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LAMME" corresp="UNIV-EVRY">Laboratoire de Mathématiques et Modélisation d'Évry</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-EVRY-SACLAY" corresp="UNIV-PARIS-SACLAY">UNIV-EVRY-SACLAY</idno>
            <idno type="stamp" n="INRAE">Institut National de Recherche en Agriculture, Alimentation et Environnement</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="GS-LIFE-SCIENCES-HEALTH" corresp="UNIVERSITE-PARIS-SACLAY">Graduate School Life Sciences and Health</idno>
            <idno type="stamp" n="MATHNUM">Département MathNum</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">The extended Eulerian numbers over function fields</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Abdelmejid</forename>
                    <surname>Bayad</surname>
                  </persName>
                  <email type="md5">47b1a05659d86036d732b65eb30913b1</email>
                  <email type="domain">univ-evry.fr</email>
                  <idno type="idhal" notation="numeric">1251167</idno>
                  <idno type="halauthorid" notation="string">2800414-1251167</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8003-335X</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-0867-8305</idno>
                  <idno type="IDREF">https://www.idref.fr/06885871X</idno>
                  <idno type="VIAF">https://viaf.org/viaf/200933408</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000431595166</idno>
                  <affiliation ref="#struct-419361"/>
                  <affiliation ref="#struct-1002387"/>
                  <affiliation ref="#struct-300306"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Mounir</forename>
                    <surname>Hajli</surname>
                  </persName>
                  <idno type="halauthorid">2014829-0</idno>
                  <affiliation ref="#struct-1059435"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">102973</idno>
                <idno type="issn">1452-8630</idno>
                <idno type="eissn">2406-100X</idno>
                <title level="j">Applicable Analysis and Discrete Mathematics</title>
                <imprint>
                  <publisher>Department of Applied Mathematics, University of Belgrade</publisher>
                  <biblScope unit="volume">16</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">508-523</biblScope>
                  <date type="datePub">2022</date>
                </imprint>
              </monogr>
              <idno type="doi">10.2298/AADM210930019B</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-nt">Mathematics [math]/Number Theory [math.NT]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this article, we introduce the extended Eulerian numbers for a large class of zeta functions, which includes the zeta functions associated to function fields, and to schemes over finite fields. This construction generalizes the extended Eulerian numbers defined by Carlitz. We give an asymptotic expansion for the summatory function associated to these numbers. Our main result generalizes the well known result on the asymptotic behavior of the extended Eulerian numbers associated to the Riemann zeta function.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1002387" status="VALID">
          <idno type="IdRef">201060213</idno>
          <idno type="RNSR">201420648M</idno>
          <idno type="ROR">https://ror.org/03jca6281</idno>
          <idno type="Wikidata">Q51781798</idno>
          <orgName>Laboratoire de Mathématiques et Modélisation d'Evry</orgName>
          <orgName type="acronym">LaMME</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>IBGBI, 23 boulevard de France91037 Evry</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math-evry.cnrs.fr/doku.php</ref>
          </desc>
          <listRelation>
            <relation active="#struct-179741" type="direct"/>
            <relation active="#struct-300306" type="direct"/>
            <relation active="#struct-419361" type="direct"/>
            <relation name="UMR8071" active="#struct-441569" type="direct"/>
            <relation name="UMR8071" active="#struct-577435" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300306" status="VALID">
          <idno type="IdRef">030820529</idno>
          <idno type="ISNI">0000000121805818</idno>
          <idno type="ROR">https://ror.org/00e96v939</idno>
          <idno type="Wikidata">Q1531014</idno>
          <orgName>Université d'Évry-Val-d'Essonne</orgName>
          <orgName type="acronym">UEVE</orgName>
          <date type="start">1991-07-22</date>
          <desc>
            <address>
              <addrLine>Boulevard François Mitterrand 91025 Evry Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-evry.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-1059435" status="VALID">
          <orgName>Shangaï Jiao Tong University [Shangaï]</orgName>
          <desc>
            <address>
              <addrLine>800 Dongchuan RD. Minhang District, Shanghai</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">https://en.sjtu.edu.cn/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-179741" status="VALID">
          <orgName>Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise</orgName>
          <orgName type="acronym">ENSIIE</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ensiie.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-577435" status="VALID">
          <idno type="ROR">https://ror.org/003vg9w96</idno>
          <orgName>Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement</orgName>
          <orgName type="acronym">INRAE</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>