Toward explicit formulas for higher representation numbers of quadratic forms
Number Theory
2011-10-31 v1
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.
Cite
@article{arxiv.1110.6346,
title = {Toward explicit formulas for higher representation numbers of quadratic forms},
author = {Lynne H. Walling},
journal= {arXiv preprint arXiv:1110.6346},
year = {2011}
}