Poisson summation and packing problems
Prof. Noam Elkies
Sunday, 8 February 2015, 1:00 PM
Harvard, Science Center E
The Poisson summation formula asserts that the sum over Z of "any" function f on R equals the sum over Z of the Fourier transform of f. We give some examples and applications (including evaluations of familiar sums such as zeta(2) and
less-familiar ones like
1/2 + 1/5 + 1/10 + 1/17 + ... + 1/(n^2+1) + ...
), and then generalize to functions on R^n where for many values of n
Poisson summation underlies the best upper bounds known on the density
of packings of space by identical spheres.