<?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-01104337</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="2026-05-20T15:34:47+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A Lemma in complex function theory I</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>
            <author role="aut">
              <persName>
                <forename type="first">K</forename>
                <surname>Ramachandra</surname>
              </persName>
              <idno type="halauthorid">884171-0</idno>
              <affiliation ref="#struct-328231"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Romain</forename>
                <surname>Vanel</surname>
              </persName>
              <email type="md5">27b81e37b3f90791f5eb089228d9a592</email>
              <email type="domain">univ-grenoble-alpes.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2015-01-16 16:41:24</date>
              <date type="whenModified">2024-04-19 15:14:37</date>
              <date type="whenReleased">2015-01-16 16:43:11</date>
              <date type="whenProduced">1989-01-01</date>
              <date type="whenEndEmbargoed">2015-01-16</date>
              <ref type="file" target="https://hal.science/hal-01104337v1/document">
                <date notBefore="2015-01-16"/>
              </ref>
              <ref type="file" subtype="publisherAgreement" n="1" target="https://hal.science/hal-01104337v1/file/12Article1.pdf" id="file-1104337-1187370">
                <date notBefore="2015-01-16"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="129677">
                <persName>
                  <forename>Romain</forename>
                  <surname>Vanel</surname>
                </persName>
                <email type="md5">27b81e37b3f90791f5eb089228d9a592</email>
                <email type="domain">univ-grenoble-alpes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01104337</idno>
            <idno type="halUri">https://hal.science/hal-01104337</idno>
            <idno type="halBibtex">balasubramanian:hal-01104337</idno>
            <idno type="halRefHtml">&lt;i&gt;Hardy-Ramanujan Journal&lt;/i&gt;, 1989, Volume 12 - 1989, pp.1 - 5. &lt;a target="_blank" href="https://dx.doi.org/10.46298/hrj.1989.108"&gt;&amp;#x27E8;10.46298/hrj.1989.108&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Hardy-Ramanujan Journal, 1989, Volume 12 - 1989, pp.1 - 5. &amp;#x27E8;10.46298/hrj.1989.108&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1104337-1187370"/></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">A Lemma in complex function theory I</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>
                <author role="aut">
                  <persName>
                    <forename type="first">K</forename>
                    <surname>Ramachandra</surname>
                  </persName>
                  <idno type="halauthorid">884171-0</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 12 - 1989</biblScope>
                  <biblScope unit="pp">1 - 5</biblScope>
                  <date type="datePub">1989-01-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.46298/hrj.1989.108</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">analytic function</term>
                <term xml:lang="en">semi-circular portion</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>Continuing our earlier work on the same topic published in the same journal last year we prove the following result in this paper: If $f(z)$ is analytic in the closed disc $\vert z\vert\leq r$ where $\vert f(z)\vert\leq M$ holds, and $A\geq1$, then $\vert f(0)\vert\leq(24A\log M) (\frac{1}{2r}\int_{-r}^r \vert f(iy)\vert\,dy)+M^{-A}.$ Proof uses an averaging technique involving the use of the exponential function and has many applications to Dirichlet series and the Riemann zeta function.</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>