<?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-01104695</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="2026-05-20T15:34:11+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On Waring's Problem: $g(4)\leq20.$</title>
            <author role="aut">
              <persName>
                <forename type="first">R</forename>
                <surname>Balasubramanian</surname>
              </persName>
              <idno type="halauthorid">882249-0</idno>
              <affiliation ref="#struct-328231"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Ariane</forename>
                <surname>Rolland</surname>
              </persName>
              <email type="md5">0ffc6e52f3e757c375844ee4f773cbe7</email>
              <email type="domain">univ-grenoble-alpes.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2015-01-19 09:25:39</date>
              <date type="whenModified">2025-06-17 15:04:37</date>
              <date type="whenReleased">2015-01-19 13:16:12</date>
              <date type="whenProduced">1985-01-01</date>
              <date type="whenEndEmbargoed">2015-01-19</date>
              <ref type="file" target="https://hal.science/hal-01104695v1/document">
                <date notBefore="2015-01-19"/>
              </ref>
              <ref type="file" subtype="publisherAgreement" n="1" target="https://hal.science/hal-01104695v1/file/8Article1.pdf" id="file-1104695-1187630">
                <date notBefore="2015-01-19"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="103946">
                <persName>
                  <forename>Ariane</forename>
                  <surname>Rolland</surname>
                </persName>
                <email type="md5">0ffc6e52f3e757c375844ee4f773cbe7</email>
                <email type="domain">univ-grenoble-alpes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01104695</idno>
            <idno type="halUri">https://hal.science/hal-01104695</idno>
            <idno type="halBibtex">balasubramanian:hal-01104695</idno>
            <idno type="halRefHtml">&lt;i&gt;Hardy-Ramanujan Journal&lt;/i&gt;, 1985, Volume 8 - 1985, pp.1-40. &lt;a target="_blank" href="https://dx.doi.org/10.46298/hrj.1985.114"&gt;&amp;#x27E8;10.46298/hrj.1985.114&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Hardy-Ramanujan Journal, 1985, Volume 8 - 1985, pp.1-40. &amp;#x27E8;10.46298/hrj.1985.114&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1104695-1187630"/></licence>
            </availability>
          </publicationStmt>
          <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">On Waring's Problem: $g(4)\leq20.$</title>
                <author role="aut">
                  <persName>
                    <forename type="first">R</forename>
                    <surname>Balasubramanian</surname>
                  </persName>
                  <idno type="halauthorid">882249-0</idno>
                  <affiliation ref="#struct-328231"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">54861</idno>
                <idno type="eissn">2804-7370</idno>
                <title level="j">Hardy-Ramanujan Journal</title>
                <imprint>
                  <publisher>Hardy-Ramanujan Society</publisher>
                  <biblScope unit="volume">Volume 8 - 1985</biblScope>
                  <biblScope unit="pp">1-40</biblScope>
                  <date type="datePub">1985-01-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.46298/hrj.1985.114</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">minor arc</term>
                <term xml:lang="en">multiplicative function</term>
                <term xml:lang="en">lower bounds</term>
                <term xml:lang="en">sum of biquadrates</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</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>Refining some of the methods used by C. J. Chen in showing that $g(5)=37$, and taking advantage of the numerical computations of Thomas who showed that $g(4)\leq22$, we prove in this paper that $g(4)\leq20$.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-328231" status="VALID">
          <idno type="ROR">https://ror.org/03ht1xw27</idno>
          <orgName>Tata Institute for Fundamental Research</orgName>
          <orgName type="acronym">TIFR</orgName>
          <date type="start">1945-01-01</date>
          <desc>
            <address>
              <addrLine>Homi Bhabha Road, ColabaMumbai 400005, INDIA</addrLine>
              <country key="IN"/>
            </address>
            <ref type="url">https://www.tifr.res.in/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>