Hecke operators on half-integral weight Siegel Eisenstein series

2016/05/30 by Walling, Lynne H.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1605.09292

Abstract

We construct a basis for the space of half-integral weight Siegel Eisenstein series of level 4N where N is odd and square-free. Then we restrict our attention to those Eisenstein series generated from elements of Γ₀(4), commenting on why this restriction is necessary for our methods. We directly apply to these forms all Hecke operators attached to odd primes, and we realize the images explicitly as linear combinations of Siegel Eisenstein series. Using this information, we diagonalize the subspace of Eisenstein series generated from elements of Γ₀(4), obtaining a multiplicity-one result.

Related

• Hecke eigenvalues of Klingen--Eisenstein series of squarefree level
• Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series
• A formula for the action of Hecke operators on half-integral weight\n Siegel modular forms and applications
• On the functional equations of Siegel Eisenstein series of an odd prime level p
• Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series