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<title lang=en>On some questions related to the Gauss conjecture for function fields</title>
<creator>Aubry, Yves</creator>
<creator>Blache, Régis</creator>
<contributor>Institut de Mathématiques de Toulon - EA 2134 (IMATH) ; Université de Toulon (UTLN)</contributor>
<contributor>Institut de mathématiques de Luminy (IML) ; Centre National de la Recherche Scientifique (CNRS) - Université de la Méditerranée - Aix-Marseille 2</contributor>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 0022-314X</source>
<source>EISSN: 1096-1658</source>
<source>Journal of Number Theory</source>
<publisher>Elsevier</publisher>
<identifier>hal-00978911</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00978911</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00978911/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00978911/file/AubryBlache5_10.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00978911</source>
<source>Journal of Number Theory, Elsevier, 2008, 128 (7), pp.2053--2062. 〈10.1016/j.jnt.2007.10.014〉</source>
<identifier>DOI : 10.1016/j.jnt.2007.10.014</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2007.10.014</relation>
<language>en</language>
<subject lang=en>Functions fields</subject>
<subject lang=en>Gauss conjecture</subject>
<subject lang=en>Zeta functions</subject>
<subject lang=en>Jacobian</subject>
<subject lang=en>Hyperelliptic curves</subject>
<subject lang=en>Finite fields</subject>
<subject>11R29 ; 11R58 ; 11R11 ; 14H05</subject>
<subject>[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]</subject>
<subject>[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>We show that, for any finite field Fq , there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.</description>
<date>2008</date>
</dc>
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