Euler Factors and Local Root Numbers for Symmetric Powers of Elliptic Curves
نویسنده
چکیده
For any elliptic curve E over a number field, there is, for each n ≥ 1, a symmetric n-power L-function, defined by an Euler product, and conjecturally having a meromorphic continuation and satisfying a precise functional equation. The sign in the functional equation is conjecturally a product of local signs. Given an elliptic curve over a finite extension of some Qp, we calculate the associated Euler factor and local sign, for any n ≥ 1.
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تاریخ انتشار 2006