Decompositions of the extended Selberg class functions - Garunkštis Ramūnas; Panavas Tadas; Šimenas Raivydas (Open Mathematics, 2025)
Let F(s)F\left(s) be a function from the extended Selberg class. We consider decompositions F(s)=f(h(s))F\left(s)=f\left(h\left(s)), where ff and hh are meromorphic functions. Among other things, we show that FF is prime if and only if the greatest common divisor of the orders of all zeros and the pole of FF is 1.