Functional Equation of the Zeta Function, Hecke’s Proof
Let f be a function on R n . We shall say that f tends to 0 rapidly at infinity if for each positive integer m the function is bounded for |x| sufficiently large. Here as in the rest of this chapter, |x| is the Euclidean norm of x. Equivalently, the preceding condition can be formulated by saying that for every polypomial P (in n variables) the function Pf is bounded, or that the function is bounded, for x sufficiently large (i.e. |x| sufficiently large).
KeywordsFunctional Equation Zeta Function Number Field Ideal Class Riemann Hypothesis
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