We define epsilon factors for irreducible representations of finite general linear groups using Macdonald's correspondence. These satisfy multiplicativity, and are expressible as products Gauss sums. The tensor product related to the Rankin-Selberg gamma factors, by which we prove that can be written exterior square relate Jacquet-Shalika Langlands-Shahidi level zero supercuspidal representatio...

We prove the conjecture of Pollack and Weston on quantitative analysis level lowering congruence à la Ribet for modular forms higher weight. It was formulated studied in context integral Jacquet–Langlands correspondence anticyclotomic Iwasawa theory weight two square-free first time. use a completely different method based $$R={\mathbb {T}}$$ theorem established by Diamond–Flach–Guo Dimitrov an...

When I was asked to suggest a Bulletin article worthy of reprinting, I knew the answer right away: An Elementary Introduction to the Langlands Program by Steven Gelbart, published by the Bulletin in 1984, remains one of the best reviews of the Langlands Program, even though this subject has expanded tremendously in the intervening years. This paper has greatly influenced my own research and is ...

Let k be a non-Archimedean local field of characteristic 0. Let D be a division algebra with center k and index n. The group D∗ is a locally compact group which is compact modulo the center. Its complex irreducible representations are finite dimensional. If π is an irreducible representation of D∗ which is self-dual, i.e., if π∨ denotes the dual of π, π∨ ∼= π, then there exists a D∗-invariant, ...