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 $leq 1/d$ of the $L$-functions of any degree $dgeq 1$ in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
Twists and resonance of L-functions, I
KACZOROWSKI, J;PERELLI, ALBERTO
2016-01-01
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 $leq 1/d$ of the $L$-functions of any degree $dgeq 1$ in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
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