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Let  K  be a number field containing the  n -th roots of unity for some  n ≥3. We prove a uniform subconvexity result for a family of double Dirichlet series built out of central values of Hecke  L -functions of  n -th-order characters of  K . The main new ingredient, possibly of independent interest, is a large sieve for  n -th-order characters. As further applications of this tool, we derive several results concerning  L ( s , χ ) with  χ  and  n -th-order Hecke character: an estimate of the second moment on the critical line, a nonvanishing result at the central point, and a zero-density theorem.

L -Functions with n -th-Order Twists