Lifting puzzles and congruences of Ikeda and Ikeda-Miyawaki lifts. (English) Zbl 1422.11109

Dummigan, Neil

J. Math. Soc. Japan 69, No. 2, 801-818 (2017).

Summary: We show how many of the congruences between Ikeda lifts and non-Ikeda lifts, proved by Katsurada, can be reduced to congruences involving only forms of genus 1 and 2, using various liftings predicted by Arthur’s multiplicity conjecture. Similarly, we show that conjectured congruences between Ikeda-Miyawaki lifts and non-lifts can often be reduced to congruences involving only forms of genus 1, 2 and 3.

MSC:

11F46

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Keywords:

congruences of automorphic forms; Ikeda lift; Ikeda-Miyawaki lift