untitled
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<identifier>oai:HAL:hal-00551470v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>L-functions of exponential sums on curves over rings</title>
<creator>Blache, Régis</creator>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 1071-5797</source>
<source>EISSN: 1090-2465</source>
<source>Finite Fields and Their Applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-00551470</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551470</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551470/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00551470/file/Charlefinal.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00551470</source>
<source>Finite Fields and Their Applications, Elsevier, 2009, 15 (3), pp.345-359. 〈10.1016/j.ffa.2009.01.001〉</source>
<identifier>DOI : 10.1016/j.ffa.2009.01.001</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ffa.2009.01.001</relation>
<language>en</language>
<subject lang=en>Exponential sums over p-adic rings</subject>
<subject lang=en>L-functions</subject>
<subject lang=en>Weil numbers</subject>
<subject lang=en>Witt vectors</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/article</type>
<type>Journal articles</type>
<description lang=en>Let C be a smooth curve over a Galois ring R. Let f be a function over C, and Ψ be an additive character of order p^l over R; in this paper we study the exponential sums associated to f and Ψ over C, and their L-functions. We show the rationality of the L-functions in a more general setting, then in the case of curves we express them as products of L-functions associated to polynomials over the affine line, each factor coming from a singularity of f. Finally we show that in the case of Morse functions (i.e. having only simple singularities), the degree of the L-functions are, up to sign, the same as in the case of finite fields, yielding very similar bounds for exponential sums.</description>
<date>2009</date>
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