A
Voronoi-style formula for GL(3)

•__Theorem
(Miller-Schmid, 2002)__ Under the same hypothesis, but instead with am,n the Fourier
coefficients of a cusp form on GL(3,Z)nGL(3,R)

for any q >
0 and

•The proof uses automorphic distributions on N(Z)n N(R), where N is the 3-dimensional Heisenberg group.

•The summation formula
reflects identities which are satisfied by the various Fourier components.

•The theorem can be
applied to GL(2) via the symmetric square
lift GL(2)! GL(3), giving nonlinear summation formulas (i.e. involving an2). This formula
is used by Sarnak-Watson in
their sharp bounds for L4-norms of
eigenfunctions on SL(2,Z)nH.