Resumen de Liftings and mean value theorems for automorphic L-functions

Kohji Matsumoto

• A general mean value theorem for Dirichlet series, with a sharp error estimate near the boundary of the critical strip, is proved. Applications of this theorem to various automorphic $L$-functions are discussed. Moreover, sharp upper bounds of mean square values of $L$-functions are obtained when they are attached to lifted forms, such as Doi¿Naganuma and Ikeda lifts in the theory of Siegel modular forms.