2016/08/08 by Wong, Tian An
#11F72 #11M26 #11M36 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1608.02296
The continuous spectrum to the spectral side of the Arthur-Selberg trace formula is described in terms of intertwining operators, whose normalising factors involve quotients of L-functions. In this paper, we derive two expressions in the case of SL(2) over a number field in terms of the Riemann-Weil explicit formula: as a sum over zeroes of the associated L-functions, and as a sum of adelic distributions on Weil groups. As an application, we obtain an expression for a lower bound for the sums over zeroes with respect to the truncation parameter for Eisenstein series.