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$L$-FUNCTIONS IN THE EXTENDED SELBERG CLASS
This paper concerns the problem of algebraic differential independence of the gamma function and 
${\mathcal{L}}$-functions in the extended Selberg class. We prove that the two kinds of functions cannot satisfy a class of algebraic differential equations with functional coefficients that are linked to the zeros of the 
${\mathcal{L}}$-function in a domain 
$D:=\{z:0<\text{Re}\,z<\unicode[STIX]{x1D70E}_{0}\}$ for a positive constant 
$\unicode[STIX]{x1D70E}_{0}$.
