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 rth local norm L-function of F at a point t E 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 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 trans-lations or homotheties.
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机译：对于在有限域k和整数r≤1上的交换代数群G上的给定l-adic捆F，我们定义了在点t E G（k）上F的第r个局部范数L函数，并证明了它的合理性。此函数提供有关范数t在G（kr）点（其中kr是k的度r的扩展）上F的局部Frobenius迹线之和的信息。对于G，一维仿射线或圆环，这些和又可以用于估计曲线上的有理点的数量或指数和的绝对值，这些值在一大组平移或相似性下是不变的。
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