Twists and resonance of L-functions, I
Abstract
We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents ≤ 1/d of the L-functions of any degree d ≥ 1 in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
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