Hisa-aki Kawamura

Ikeda's conjecture on the period of the Ikeda lifting

As one of the most fascinating problems in the theory of modular forms, we study the relation between the periods (or the Petersson inner products) of cuspidal Hecke eigenforms which are related with each other through their L-functions. In particular, there are several important results concerning the relation between the period of a cuspidal Hecke eigenform with respect to elliptic modular group and a certain lifting of it, for example, K. Doi, H. Hida and H. Ishii obtained such a relation for the Doi-Naganuma lifting. In this talk, we would like to report our recent achievement of the proof of T. Ikeda's conjecture on the period of the Ikeda lifting which is a generalization of the Saito-Kurokawa lifting to higher degree. This is a joint work with H. Katsurada.