Journal of the European Mathematical Society
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Twists and resonance of $L$-functions, IJerzy Kaczorowski and Alberto Perelli (1) Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614, Poznan, Poland
(2) DIMA - Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy
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.
Keywords: $L$-functions, Selberg class, twists, resonance
Kaczorowski Jerzy, Perelli Alberto: Twists and resonance of $L$-functions, I. J. Eur. Math. Soc. 18 (2016), 1349-1389. doi: 10.4171/JEMS/616