Functional Equation of the Zeta Function, Hecke’s Proof

Abstract

Let f be a function on Rⁿ. We shall say that f tends to 0 rapidly at infinity if for each positive integer m the function

$$x\; \mapsto \;(1 + \left| x \right|)^m f(x),\quad \quad \quad \quad \quad \quad \quad x \in R^n,$$

is bounded for |x| sufficiently large.