On the rationality of period integrals and special value formulas in the compact case (Q776973)

Motivated by special value formulas for automorphic \(L\)-functions, particularly the Gan-Gross-Prasad conjecture, the authors study period integrals associated to adelic automorphic forms for algebraic groups satisfying a certain compactness condition. They prove that when restricted to a suitable subspace of ``algebraic automorphic forms'' [\textit{B. H. Gross}, Isr. J. Math. 113, 61--93 (1999; Zbl 0965.11020)], the corresponding period integrals are ``rational'' in a certain technical sense. For the precise results and applications to central value formulas for convolution \(L\)-functions, which require quite a bit of notation and terminology, we refer to the present paper's introduction.