Euler-Stieltjes constants for the Rankin-Selberg L-function and weighted Selberg orthogonality
. Let E be Galois extension of Q of finite degree and let π and π ′ be two irreducible automorphic unitary cuspidal representations of GL m ( E A ) and GL m ′ ( E A ), respectively. We prove an asymptotic formula for computation of coefficients γ π,π ′ ( k ) in the Laurent (Taylor) series expansion around s = 1 of the logarithmic derivative of the Rankin-Selberg L − function L ( s,π × e π ′ ) under assumption that at least one of representations π , π ′ is self-contragredient and show that coefficients γ π,π ′ ( k ) are related to weighted Selberg orthogonality. We also replace the assumption that at least one of representations π and π ′ is self-contragredient by a weaker one.