Thursday 05 Dec 2019NT Seminar: Representing quadratic forms by other quadrtic forms

Prof. Lynne Walling - University of Bristol

H103 14:30-16:30

A classical question in number theory is: given a positive integer n,

how many ways can we represent n as a sum of k integer squares?

This question has been approached using the theory of modular forms, and in some 

cases this approach has yielded some beautiful formulas.  In the 1930's, Siegel

generalised this question: given a lattice L with a positive definite quadratic form q,

and given another quadratic form q', on how many sublattices of L does q restrict

to q'?  We will explore this question using the theory of Siegel modular forms;

in particular, we will use Siegel's generalised theta series and Siegel-Eisenstein series.

We will discuss how to construct these latter two sorts of objects, and precisely

how they relate to each other.


We will not assume knowledge of modular forms.

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