Pullback of Klingen Eisenstein series and certain critical L-values identities

TL;DR

This paper derives pullback formulas for Klingen Eisenstein series at various levels and uses them to establish identities relating to critical L-values of modular forms.

Contribution

It introduces new pullback formulas for Klingen Eisenstein series at arbitrary levels and applies them to prove identities involving critical L-values.

Findings

Pullback formulas for Klingen Eisenstein series at various levels.

Identities involving critical L-values of elliptic modular forms.

Application of Fourier expansion to establish L-value identities.

Abstract

We obtain pullback formulas for Klingen Eisenstein series with arbitrary levels, with respect to both Siegel congruence and paramodular subgroups, in degree two. Pullback results are used, along with the Fourier series expansion of Klingen Eisenstein series given by Mizumoto, to prove certain identities involving critical values of $ L$-functions attached to normalized elliptic modular forms of weight $ k $ and full level.