Stieltjes constants of L-functions in the extended Selberg class.

Let f be an arithmetic function and let S # denote the extended Selberg class. We denote by L ( s ) = ∑ n = 1 ∞ f ( n ) n s the Dirichlet series attached to f. The Laurent-Stieltjes constants of L ( s ) , which belongs to S # , are the coefficients of the Laurent expansion of L at its pole s = 1 . In this paper, we give an upper bound of these constants, which is a generalization of many known results.