Article
Rationality of trace and norm L-functions
Author/s | Rojas León, Antonio |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2012-06-15 |
Deposit Date | 2016-06-07 |
Published in |
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Abstract | 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 ... 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. |
Project ID. | P08-FQM-03894
MTM2007-66929 |
Citation | Rojas León, A. (2012). Rationality of trace and norm L-functions. Duke Mathematical Journal, 161 (9), 1751-1795. |
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