Abstract
It is known that average Siegel theta series lie in the space of Siegel
Eisenstein series. Also, every lattice equipped with an even integral quadratic form
lies in a maximal lattice. Here we consider average Siegel theta series of degree 2
attached to maximal lattices; we construct maps for which the average theta series
is an eigenform. We evaluate the action of these maps on Siegel Eisenstein series of
degree 2 (without knowing their Fourier coefficients), and then realise the average
theta series as an explicit linear combination of the Eisenstein series.
| Translated title of the contribution | Toward explicit formulas for higher representation numbers of quadratic forms |
|---|---|
| Original language | English |
| Number of pages | 53 |
| Journal | arXiv |
| Publication status | Published - 2012 |