This is the second of four lectures given about "Quadratic Forms and Automorphic Forms" at the 2009 Arizona Winter School, to an audience of interested graduate students. Detailed notes supporting these lectures are available at: arxiv.org/abs/1105.5759
This lecture introduces theta functions as a tool to understand representations questions about quadratic forms, describes how they fit within the theory of modular forms, and gives some explicit quantitative local-global results of Siegel for understanding the "average" theta series of quadratic forms in a given genus.
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