The base change \(L\)-function for modular forms and beyond endoscopy
In the paper under review, the author studies \(L\)-functions arising from base change in the case of a modular form using the trace formula, building on ideas of \textit{R. P. Langlands} [in: Contributions to automorphic forms, geometry, and number theory. Johns Hopkins University, Baltimore, USA, 2002. Baltimore, MD: Johns Hopkins University Press. 611--697 (2004; Zbl 1078.11033)] and \textit{P. Sarnak} [``Comments on Robert Langlands lecture: `Endoscopy and Beyond' '', Letter (2001)] on the \textit{beyond endoscopy} program.NEWLINENEWLINEIn the case of quadratic base change for real fields, the introduced methods enable the author to provide a new proof of the absolute convergence and analytic continuation of the studied \(L\)-functions in appropriate right half planes.
scientific article; zbMATH DE number 6334890