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Let K be a number field containing the n-th roots of unity for some n > 2. Weprove a uniform subconvexity result for a family of double Dirichlet seriesbuilt 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 forn-th order characters. As further applications of this tool, we derive severalresults concerning L(s,\chi) for n-th order Hecke characters: an estimate ofthe second moment on the critical line, a non-vanishing result at the centralpoint, and a zero-density theorem.

L-functions with n-th order twists