Toward explicit formulas for higher representation numbers of quadratic forms

Research output: Contribution to journalArticle (Academic Journal)peer-review

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 contributionToward explicit formulas for higher representation numbers of quadratic forms
Original languageEnglish
Number of pages53
JournalarXiv
Publication statusPublished - 2012

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