Congruences to Ikeda-Miyawaki lifts and triple L-values of elliptic modular forms

In this paper, we consider congruences between the Ikeda-Miyawaki lift and other Siegel modular forms, relating these congruences to critical values of L-functions by using Ikedaʼs conjecture on periods. We also give general formulas for critical values of triple L-functions and prove results, both in theory and in examples, on the relation between such congruences and critical values.