2015/12/31 by Altug, Salim Ali · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1512.09249
We finalize the analysis of the trace formula initiated in \citeAltug:2015aa and developed in \citeAltug:2015ab, and calculate the asymptotic expansion of the beyond endoscopic averages for the standard L-functions attached to weight k≥3 cusp forms on GL(2) (cf. Theorem \refmainthm). This, in particular, constitutes the first example of beyond endoscopy executed via the Arthur-Selberg trace formula, as originally proposed in \citeLanglands:2004aa. As an application we also give a new proof of the analytic continuation of the L-function attached to Ramanujan's Δ-function.