Euler Factors and Local Root Numbers for Symmetric Powers of Elliptic Curves
Euler Factors and Local Root Numbers for Symmetric Powers of Elliptic Curves
For any elliptic curve E over a number field, there is, for each n ≥ 1, a symmetric n th -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 …