untitled
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<identifier>oai:HAL:hal-00551461v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<setSpec>collection:UNIV-AG</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Newton polygons for character sums and Poincaré series</title>
<creator>Blache, Régis</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>accepté pour publication par l'International Journal of Number Theory</description>
<identifier>hal-00551461</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551461</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551461/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551461/file/prodpolytopespubli.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00551461</source>
<source>accepté pour publication par l'International Journal of Number Theory. 2011</source>
<language>en</language>
<subject lang=en>Character sums</subject>
<subject lang=en>$L$-functions</subject>
<subject lang=en>Newton polygons and polytopes</subject>
<subject>11M38,13A02,52B20</subject>
<subject>[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]</subject>
<subject>[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]</subject>
<type>info:eu-repo/semantics/preprint</type>
<type>Preprints, Working Papers, ...</type>
<description lang=en>In this paper, we precise the asymptotic behaviour of Newton polygons of $L$-functions associated to character sums, coming from certain $n$ variable Laurent polynomials. In order to do this, we use the free sum on convex polytopes. This operation allows the determination of the limit of generic Newton polygons for the sum $Delta=Delta_1oplus Delta_2$ when we know the limit of generic Newton polygons for each factor. To our knowledge, these are the first results concerning the asymptotic behaviour of Newton polygons for multivariable polynomials when the generic Newton polygon differs from the combinatorial (Hodge) polygon associated to the polyhedron.</description>
<date>2011-01-03</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
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