Starting with Green’s functions on adele points of GL(2) considered over a
totally real number field, we elaborate an explicit version of the relative trace for-
mula, whose spectral side encodes the informaton on period integrals of cuspidal
waveforms along a maximal split torus. As an application, we prove two kinds of as-
ymptotic mean formula for certain central L-values attached to cuspidal waveforms
with square-free level.
Received by the editor April 8, 2010 and, in revised form, April 11, 2013.
Article electronically published on October 24, 2014.
2010 Mathematics Subject Classification. Primary 11F72; Secondary 11F67, 11F36.
2014 American Mathematical Society