Opened Access Rationality of trace and norm L-functions


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Autor: Rojas León, Antonio
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2012-06-15
Publicado en: Duke Mathematical Journal, 161 (9), 1751-1795.
Tipo de documento: Artículo
Resumen: For a given l-adic sheaf F on a commutative algebraic group G over a finite field k and an integer r ≥ 1 we define the r-th local norm Lfunction of F at a point t ∈ G(k) and prove its rationality. This function gives information on the sum of the local Frobenius traces of F over the points of G(kr) (where kr is the extension of degree r of k) with norm t. For G the onedimensional affine line or the torus, these sums can in turn be used to estimate the number of rational points on curves or the absolute value of exponential sums which are invariant under a large group of translations or homotheties.
Cita: Rojas León, A. (2012). Rationality of trace and norm L-functions. Duke Mathematical Journal, 161 (9), 1751-1795.
Tamaño: 489.0Kb
Formato: PDF


DOI: 10.1215/00127094-1593371

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