The
distributional vantage point

•The Voronoi summation
formula is simply the statement
that the distribution t(x) is automorphic…integrated
against test functions.

•Namely,

•Integrate against
g^(x), and get

•This is equivalent to
the Voronoi formula.

•To justify the proof,
use the oscillation of t(x) near rationals
(as in the analytic continuation of L(s,t)).