As shown by Michel-Ramakrishan (2007) and later generalized by
Feigon-Whitehouse (2008), there are "stable" formulas for the average central
L-value of the Rankin-Selberg convolutions of some holomorphic forms of fixed
even weight and large level against a fixed imaginary quadratic theta series.
We obtain exact finite formulas for twisted first moments of Rankin-Selberg
L-values in much greater generality and prove analogous "stable" formulas when
one considers either arbitrary modular twists of large prime power level or
real dihedral twists of odd type associated to a Hecke character of mixed
signature.Comment: 25 pages; typos corrected in corollaries to Thm 1.2, substantial
details added to Sec 2.2--2.3, minor changes throughou
