Local theta correspondence and the lifting of Duke, Imamoglu and Ikeda

TL;DR

This paper uses local theta correspondence results to show that for large degrees, the Duke-Imamoglu-Ikeda lift of an elliptic modular form cannot be expressed as a linear combination of theta series.

Contribution

It demonstrates a new non-representability result for Duke-Imamoglu-Ikeda lift in terms of theta series using local theta correspondence techniques.

Findings

Duke-Imamoglu-Ikeda lift is not a linear combination of theta series for large degrees.

The proof relies on properties of local theta correspondence.

Provides insight into the structure of lifts in automorphic forms.

Abstract

We use results on the local theta correspondence to prove that for large degrees the Duke-Imamoglu-Ikeda lifting of an elliptic modular form is not a linear combination of theta series.