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

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
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