Geodesic
Internal twists of $L$-functions. II
Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 127-143.

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A nonlinear twist $F(s;f)$ of a function $F(s)$ from the extended Selberg class $\mathcal S^\sharp $ is called internal if it belongs to $\mathcal S^\sharp $. In a previous paper (2014) we showed that, inside a rather general class of nonlinear twists, the internal twists occur only in very special cases; moreover, we gave a first characterization of such twists. Here we complete our previous work by giving a fully detailed description of such internal twists.
Keywords: $L$-functions, Selberg class, twists. 
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J. Kaczorowski; A. Perelli. Internal twists of $L$-functions. II. Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 127-143. http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a7/

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