##\theta(\tau, A) = \sum\limits_{\vec{x}\in Z^{m}} e^{\pi i A[x] \tau } ##(adsbygoogle = window.adsbygoogle || []).push({});

##=\sum\limits^{\infty}_{n=0} r_{A}(n)q^{n} ##,

where ## r_{A} = No. [ \vec{x} \in Z^{m} ; A[\vec{x}] =n]##

where ##A[x]= x^t A x ##, is the associated quadratic from to the matrix ##A##, where here ##A## is positive definite, of rank ##m## and even. (and I think symmetric?)

So I thought that this meant to solve the quadratic ##A[x]= \vec{x^t} A \vec{x} = n ##, for each ##n##, and the representation number is then given by the number of solutions to this?, subject to ## \vec{x} \in Z^{m} ## ,

What is ##Z^{m}## here please? ( z the integer symbol)

Many thanks

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# A Representation number via quad forms of theta quadratic form

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