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2013 | OriginalPaper | Buchkapitel

Quadratic Forms and Automorphic Forms

verfasst von : Jonathan Hanke

Erschienen in: Quadratic and Higher Degree Forms

Verlag: Springer New York

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Abstract

These notes give a friendly four-part introduction to various aspects of the arithmetic and analytic theories of quadratic forms, aimed at a graduate-level audience. The main themes discussed are: geometry and local-global methods, theta functions and Siegel’s theorem, Clifford algebras and spin groups, and adelic theta liftings via the Weil representation.

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Vorheriges Kapitel Weighted Generating Functions for Type II Lattices and Codes

Nächstes Kapitel Integral Positive Ternary Quadratic Forms

We could also have defined an inner product using the Hessian bilinear form, but this choice is less standard in the literature and the difference will not matter for our purposes in this section.

For any subset S ⊆ V the set H(S, L) is an R-module, and so it is natural to consider maximal subsets of V where H(S, L) is a fixed R-module. From the bilinearity of H, we see that these maximal sets S are also R-modules.

To justify this, notice that both the trivial and theta multiplier systems have value 1 on this element.

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Titel: Quadratic Forms and Automorphic Forms
verfasst von: Jonathan Hanke
Verlag: Springer New York
Buch: Quadratic and Higher Degree Forms
Print ISBN: 978-1-4614-7487-6

Electronic ISBN: 978-1-4614-7488-3

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-1-4614-7488-3_5

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