Tate’s Thesis

  • Anton Deitmar
Part of the Universitext book series (UTX)


Tate’s thesis from 1950 is a milestone in number theory. Fourier analysis on adeles and ideles is applied to construct meromorphic extension of L-functions. In this chapter we give its main contents with full proofs in the simplest case of the number field ℚ. The main technical ingredient is the Poisson summation formula, which is also proven here.


Prime Ideal Galois Group Automorphic Form Galois Representation Galois Extension 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Anton Deitmar
    • 1
  1. 1.Inst. MathematikUniversität TübingenTübingenGermany

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