Nonvanishing of Dirichlet L-functions on the line one

ID: nonvanishing-of-dirichlet-l-functions-on-the-line-one

For a nonprincipal Dirichlet character, the line is zero-free. Euler product positivity for L-function nonvanishing proves this for nonreal characters at every height, and for all characters at nonzero height, where a possibly principal squared-character factor has no pole. The point of height zero is the nonvanishing of nonprincipal Dirichlet L-functions at one. A principal L-function has a pole at one, and no zeros at the other points of this line.

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