Linear dependence of certain L-values of half-integral weight modular forms

Let h be a cusp form of half-integral weight, and epsilon((x))(3/2) be a certain (not necessarily holomorphic) modular form of weight 3/2 associated with a Dirichlet character.. We then prove linear dependence of the values R(l, h, epsilon((x))(3/2)) of the Rankin-Selberg convolution products of h and epsilon((x))(3/2) when we fix an integer l and vary.. A main idea for the proof is to express such a convolution product as the twisted Koecher-Maass series L( s, M( h),.) for the Maass lift M( h) of h, whose values at integers were investigated by Choie and Kohnen. Moreover, by using such an expression, we obtain an algebraicity result for the values of L( s, M( h),.) at half-integers, which was not considered by Choie and Kohnen.