The Selberg class of L-functions: non-linear twists

In a paper published in 1992, Selberg introduced an axiomatic class of L-functions (now called the Selberg class S) and raised several very interesting problems. In particular, Selberg raised the problem of classifying the L-functions in S. In this talk we first review the results on the classification problem. Such results depend on the analytic properties of the linear twists of the L-functions. Then we introduce certain non-linear twists and present some recent work (joint with J.Kaczorowski) on their analytic properties and applications.