We show that the Hilbert subspace of L2(G(F)?G(A)) generated by wave packets Eisenstein series built from discrete is whole space. Together with work Lapid [17], it achieves a proof spectral theorem R.P. Langlands ([16], [19]) based on J. Bernstein and E. [6] meromorphic continuation data. I use truncation compact sets as Arthur did for local trace formula in [2].

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

In this note, we study conjectures of Artin and Langlands and derive the automorphy of all solvable groups of order at most 200, three groups excepted.

26 NOTICES OF THE AMS VOLUME 47, NUMBER 1 H armonic analysis can be interpreted broadly as a general principle that relates geometric objects and spectral objects. The two kinds of objects are sometimes related by explicit formulas, and sometimes simply by parallel theories. This principle runs throughout much of mathematics. The rather impressionistic table at the top of the opposite page prov...

We prove a realization of the local Langlands correspondence for two-dimensional representations Weil group conductor three in cohomology Lubin–Tate curves by purely geometric method.

Matthew Lomasa, Victoria Rickarda, Fraser Miltonb, Sharon Savageb, Andrew Weirc & Adam Zemana*a College of Medicine and Health, House, University Exeter, UKb School Psychology, Life Environmental Sciences, Washington Singer, UKc Institute Neurological Langlands Drive, Glasgow, UK