Tate's thesis
Using harmonic analysis, more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the Hecke L-function.Erich Hecke used a generalized theta series associated to an algebraic number field and a lattice in its ring of integers.Kenkichi Iwasawa independently discovered essentially the same method (without an analog of the local theory in Tate's thesis) during the Second World War and announced it in his 1950 International Congress of Mathematicians paper and his letter to Jean Dieudonné written in 1952.Iwasawa in his letter to Dieudonné derived on several pages not only the meromorphic continuation and functional equation of the L-function, he also proved finiteness of the class number and Dirichlet's theorem on units as immediate byproducts of the main computation.The theory in positive characteristic was developed one decade earlier by Ernst Witt, Wilfried Schmid, and Oswald Teichmüller.