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Twists and resonance of \(L\)-functions. I. (English) Zbl 1404.11107

In the paper, nonlinear twists with exponents \(\leq \dfrac{1}{d}\) of the \(L\)-functions of any degree \(d \geq 1\) in the extended Selberg class \(S^\#\) are studied, i.e., the meromorphic continuation, polar structure and certain bounds for the order of growth are obtained. Note that this solves the resonance problem.
The paper is a continuation of previous works by the authors [Acta Math. 182, No. 2, 207–241 (1999; Zbl 1126.11335; Acta Arith. 116, No. 4, 315–341 (2005; Zbl 1082.11055); Ann. Math. (2) 173, No. 3, 1397–1441 (2011; Zbl 1235.11085)].

MSC:

11M41 Other Dirichlet series and zeta functions
11L07 Estimates on exponential sums
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References:

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