Feeds:
Posts
$\theta(z;\tau) = \sum_{n=-\infty}^\infty \exp(\pi i n^2\tau + 2 \pi i n z)$
which for $t=i\tau$ is the fundamental solution of the heat equation of the circle.  The fundamental solution of the heat equation for Dirac-squared on the 4-sphere differs from this spectrally as from the integers we have to remove 0, +/-1.  The heat kernel itself will involve eigenspinors replacing the trigonometric functions in the latter case as well but the spectral difference is probably extremely significant for issues of zeta function and analytic number theory which I might return to.