Beyond Endoscopy via the trace formula - III: The standard representation
Abstract
We finalize the analysis of the trace formula initiated in Altug:2015aa and developed in Altug: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 mainthm). This, in particular, constitutes the first example of beyond endoscopy executed via the Arthur-Selberg trace formula, as originally proposed in Langlands:2004aa. As an application we also give a new proof of the analytic continuation of the L-function attached to Ramanujan's -function.
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