Modular Forms and ℓ-Adic Representations

  • R. P. Langlands
Part of the Lecture Notes in Mathematics book series (LNM, volume 349)


This report is another attempt on the part of its author to come to terms with the circumstance that L-functions can be introduced not only in the context of automorphic forms, with which he has had some experience, but also in the context of diophantine geometry. That this circumstance can be the source of deep problems was, I believe, first perceived by E. Artin. He was, to be sure, concerned with forms on GL(1) and with varieties of dimension 0. This remains the only case in which results of any profundity have been obtained. These have been hard won. Their mathematical germ is the theory of cyclotomic fields; itself easy-only in comparison to the general theory.


Exact Sequence Cohomology Group Galois Group Trace Formula Automorphic Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • R. P. Langlands
    • 1
  1. 1.Institute for Advanced Study PrincetonNew JerseyUSA

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