Objective This proposal is at the interface of number theory and automorphic forms and aims at a cross-fertilization of both areas. It focuses on explicit arithmetic problems that can be solved using the full force of the automorphic machinery. Conversely it develops the theory of automorphic forms in higher rank using number theoretic methods.At the core are three sets of deep and longstanding open conjectures in higher rank cases:- the joint equidistribution conjectures of Michel and Venkatesh concerning the distribution of pairs of shifted CM points,- the “beyond endoscopy” program of Langlands of identifying functional lifts by a comparison of different trace formulae,- the density and optimal lifting conjectures of Sarnak concerning the behaviour of exceptional eigenvalues, and their arithmetic consequences.The key objects are certain Shimura varieties associated to abelian varieties, higher rank Kloosterman sums, families of L-functions, trace formulae and Hecke eigenvalues.By an interdisciplinary combination of analytic number theory and automorphic forms, the proposal aims at definitive progress and solutions to these three conjectures, each of which has been open for at least 15 years. Fields of science natural sciencesmathematicspure mathematicsarithmeticsL-functions Keywords Automorphic forms analytic number theory trace formulae equidistribution L-functions beyond endoscopy Kloosterman sums density theorems Programme(s) HORIZON.1.1 - European Research Council (ERC) Main Programme Topic(s) ERC-2021-ADG - ERC ADVANCED GRANTS Call for proposal ERC-2021-ADG See other projects for this call Funding Scheme ERC - Support for frontier research (ERC) Coordinator RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Net EU contribution € 1 956 665,00 Address Regina pacis weg 3 53113 Bonn Germany See on map Region Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
