## Journal of the Mathematical Society of Japan

### Lifting puzzles and congruences of Ikeda and Ikeda–Miyawaki lifts

Neil DUMMIGAN

#### Abstract

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.

#### Article information

Source
J. Math. Soc. Japan, Volume 69, Number 2 (2017), 801-818.

Dates
First available in Project Euclid: 20 April 2017

https://projecteuclid.org/euclid.jmsj/1492653647

Digital Object Identifier
doi:10.2969/jmsj/06920801

Mathematical Reviews number (MathSciNet)
MR3638285

Zentralblatt MATH identifier
06737034

#### Citation

DUMMIGAN, Neil. Lifting puzzles and congruences of Ikeda and Ikeda–Miyawaki lifts. J. Math. Soc. Japan 69 (2017), no. 2, 801--818. doi:10.2969/jmsj/06920801. https://projecteuclid.org/euclid.jmsj/1492653647

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