ERC Advanced Grant
Automorphic Forms and Arithmetic (AuForA)
Principal investigator: Valentin Blomer
The field of research 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. This includes the joint equidistribution conjectures of Michel and Venkatesh, progress on the Langlands' "beyond endoscopy" program and the density and optimal lifting conjectures of Sarnak. The key objects are certain Shimura varieties, higher rank Kloosterman sums, families of L-functions, trace formulae and Hecke eigenvalues. The methods feature an interdisciplinary combination of analytic number theory and automorphic representation theory.