Algebraicity of critical values of adjoint L-functions for GSp(4)

We prove an algebraicity result for certain critical value of adjoint L-functions for GSp ₄ over a totally real number field in terms of the Petersson norm of normalized generic cuspidal newforms on GSp ₄ . As an application, we establish an algebraic version of the Lapid–Mao conjecture for Whittaker–Fourier coefficients of cusp forms on GSp ₄ .