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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">A relation between automorphic forms on <italic>GL</italic>(2) and <italic>GL</italic>(3)</title><author><name sortKey="Gelbart, Stephen" sort="Gelbart, Stephen" uniqKey="Gelbart S" first="Stephen" last="Gelbart">Stephen Gelbart</name><affiliation><nlm:aff id="af1">Department of Mathematics, Cornell University, Ithaca, New York 14853</nlm:aff></affiliation></author><author><name sortKey="Jacquet, Herve" sort="Jacquet, Herve" uniqKey="Jacquet H" first="Hervé" last="Jacquet">Hervé Jacquet</name><affiliation><nlm:aff id="af2">Department of Mathematics, Columbia University, New York, N.Y. 10027</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">16592351</idno><idno type="pmc">431110</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC431110</idno><idno type="RBID">PMC:431110</idno><date when="1976">1976</date><idno type="wicri:Area/Pmc/Corpus">000043</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000043</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">A relation between automorphic forms on <italic>GL</italic>(2) and <italic>GL</italic>(3)</title><author><name sortKey="Gelbart, Stephen" sort="Gelbart, Stephen" uniqKey="Gelbart S" first="Stephen" last="Gelbart">Stephen Gelbart</name><affiliation><nlm:aff id="af1">Department of Mathematics, Cornell University, Ithaca, New York 14853</nlm:aff></affiliation></author><author><name sortKey="Jacquet, Herve" sort="Jacquet, Herve" uniqKey="Jacquet H" first="Hervé" last="Jacquet">Hervé Jacquet</name><affiliation><nlm:aff id="af2">Department of Mathematics, Columbia University, New York, N.Y. 10027</nlm:aff></affiliation></author></analytic><series><title level="j">Proceedings of the National Academy of Sciences of the United States of America</title><idno type="ISSN">0027-8424</idno><idno type="eISSN">1091-6490</idno><imprint><date when="1976">1976</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Let ρ<sub><italic>n</italic></sub> denote the standard n-dimensional representation of <italic>GL(n</italic>,C) and ρ<sub><italic>n</italic></sub><sup>2</sup> its symmetric square. For each automorphic cuspidal representation π of <italic>GL</italic>(2,A) we introduce an Euler product <italic>L</italic>(<italic>s</italic>,π,ρ<sub>2</sub><sup>2</sup>) of degree 3 which we prove is entire. We also prove that there exists an automorphic representation II of <italic>GL</italic>(3)—“the lift of π”—with the property that <italic>L</italic>(<italic>s</italic>,II,ρ<sub>3</sub>) = <italic>L</italic>(<italic>s</italic>,π,ρ<sub>2</sub><sup>2</sup>). Our results confirm conjectures described in a more general context by R. P. Langlands [(1970) <italic>Lecture Notes in Mathematics</italic>, no. 170 (Springer-Verlag, Berlin-Heidelberg-New York)].</p></div></front></TEI><pmc article-type="research-article"><pmc-comment>The publisher of this article does not allow downloading of the full text in XML form.</pmc-comment>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Proc Natl Acad Sci U S A</journal-id><journal-title>Proceedings of the National Academy of Sciences of the United States of America</journal-title><issn pub-type="ppub">0027-8424</issn><issn pub-type="epub">1091-6490</issn></journal-meta><article-meta><article-id pub-id-type="pmid">16592351</article-id><article-id pub-id-type="pmc">431110</article-id><article-categories><subj-group subj-group-type="heading"><subject>Physical Sciences: Mathematics</subject></subj-group></article-categories><title-group><article-title>A relation between automorphic forms on <italic>GL</italic>(2) and <italic>GL</italic>(3)</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Gelbart</surname><given-names>Stephen</given-names></name><xref ref-type="aff" rid="af1">*</xref></contrib><contrib contrib-type="author"><name><surname>Jacquet</surname><given-names>Hervé</given-names></name><xref ref-type="aff" rid="af2">†</xref></contrib></contrib-group><aff id="af1"><label>*</label>Department of Mathematics, Cornell University, Ithaca, New York 14853</aff><aff id="af2"><label>†</label>Department of Mathematics, Columbia University, New York, N.Y. 10027</aff><pub-date pub-type="ppub"><month>10</month><year>1976</year></pub-date><volume>73</volume><issue>10</issue><fpage>3348</fpage><lpage>3350</lpage><abstract><p>Let ρ<sub><italic>n</italic></sub> denote the standard n-dimensional representation of <italic>GL(n</italic>,C) and ρ<sub><italic>n</italic></sub><sup>2</sup> its symmetric square. For each automorphic cuspidal representation π of <italic>GL</italic>(2,A) we introduce an Euler product <italic>L</italic>(<italic>s</italic>,π,ρ<sub>2</sub><sup>2</sup>) of degree 3 which we prove is entire. We also prove that there exists an automorphic representation II of <italic>GL</italic>(3)—“the lift of π”—with the property that <italic>L</italic>(<italic>s</italic>,II,ρ<sub>3</sub>) = <italic>L</italic>(<italic>s</italic>,π,ρ<sub>2</sub><sup>2</sup>). Our results confirm conjectures described in a more general context by R. P. Langlands [(1970) <italic>Lecture Notes in Mathematics</italic>, no. 170 (Springer-Verlag, Berlin-Heidelberg-New York)].</p></abstract><kwd-group><kwd><italic>L</italic>-functions attached to automorphic forms</kwd><kwd>symmetric squares and the lift of a cusp form</kwd><kwd>Langlands' philosophy of <italic>L</italic>-functions</kwd></kwd-group></article-meta></front></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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