An average of special values of Dirichlet series of Rankin-Selberg type

摘要

For an integernand a Dirichlet character xi moduloN, we denote bySn(N,xi)the space of cusp forms of weightnwith respect to Gamma 0(N)and nebentypus xi is the Hecke congruence subgroup. Letk, lbe nonnegative integers withk-l >= 2Dirichlet characters moduloN.