A new mean‐value result for Dirichlet L‐functions and polynomials

Watt's result on upper bounds for the mean value ∫‐T^T |Ζ (½+it ) |⁴ |∑m am m^‐it |² dt is generalized to cover (1)/(φ (q)) ∑χ (mod q) ∫‐T^T |L (½+it, χ ) |⁴ |∑m am χ (m) m^‐it |² dt, where χ denotes a Dirichlet character (modulo q) and L(s, χ) is the corresponding Dirichlet L‐function.