Description
Abstract: We begin with an introduction to Siegel modular forms, particularly to Siegel theta series and how their Fourier coefficients encode information about quadratic forms. Then we introduce Hecke operators and discuss their action on the Fourier coefficients of a Siegel modular form, and how they can help us understand the number theoretic information carried by these Fourier coefficients. We introduce Siegel-Eisenstein series; although we do not have (closed form) formulas for all but a few Siegel Eisenstein series, we show how we can compute the action of the Hecke operators on a basis for the space of Siegel Eisenstein series. Finally, we describe how to explicitly realise the "average" Siegel theta series attached to a quadratic form as a linear combination of Siegel Eisenstein series.