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# Documents  Walling, Lynne | enregistrements trouvés : 2

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## The ubiquitous heat Kernel :AMS special session#Oct. 2-4 Jorgenson, Jay ; Walling, Lynne | American Mathematical Society 2006

Congrès

- 402 p.
ISBN 978-0-8218-3698-9

Contemporary mathematics , 0398

Localisation : Collection 1er étage

équation de chaleur # représentation de groupe de Lie # forme de Jacobi # géométrie algébrique # théorie des opérateurs appliqués à la physique quantique # géométrie différentielle globale # théorie spectrale # polynôme # équation d'évolution géométrique # noyeau de la chaleur

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## Understanding quadratic forms on lattices through generalised theta series Walling, Lynne | CIRM H

Multi angle

Research talks;Number Theory

Siegel introduced generalised theta series to study representation numbers of quadratic forms. Given an integral lattice $L$ with quadratic form $q$, Siegel’s degree $n$ theta series attached to $L$ has a Fourier expansion supported on $n$-dimensional lattices, with Fourier coefficients that tells us how many times $L$ represents any given $n$-dimensional lattice. Siegel proved that this theta series is a type of automorphic form.
In this talk we explore how the theory of automorphic forms, together with the theory of quadratic forms, helps us understand these representation numbers. We reveal arithmetic relations between ”average” representation numbers (where we average over a genus), and finally we give an explicit formula for these average representation numbers in terms of the Fourier coefficients of Siegel Eisenstein series. In the case that $n = 1$ (meaning we are looking at how often $L$ represents an integer) this yields explicit numerical formulas for these average representation numbers.
Siegel introduced generalised theta series to study representation numbers of quadratic forms. Given an integral lattice $L$ with quadratic form $q$, Siegel’s degree $n$ theta series attached to $L$ has a Fourier expansion supported on $n$-dimensional lattices, with Fourier coefficients that tells us how many times $L$ represents any given $n$-dimensional lattice. Siegel proved that this theta series is a type of automorphic form.
In this talk ...

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