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15 June 2012 Rationality of trace and norm L-functions
Antonio Rojas-León
Duke Math. J. 161(9): 1751-1795 (15 June 2012). DOI: 10.1215/00127094-1593371

Abstract

For a given -adic sheaf F on a commutative algebraic group G over a finite field k and an integer r1, we define the rth local norm L-function of F at a point tG(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 1-dimensional 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.

Citation

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Antonio Rojas-León. "Rationality of trace and norm L-functions." Duke Math. J. 161 (9) 1751 - 1795, 15 June 2012. https://doi.org/10.1215/00127094-1593371

Information

Published: 15 June 2012
First available in Project Euclid: 6 June 2012

zbMATH: 1298.14023
MathSciNet: MR2858919
Digital Object Identifier: 10.1215/00127094-1593371

Subjects:
Primary: 14F20
Secondary: 11L07 , 11S40

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 9 • 15 June 2012
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