Algebraic Number Theory pp 245-273 | Cite as

# Functional Equation of the Zeta Function, Hecke’s Proof

Chapter

## Abstract

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).

## Keywords

Functional Equation Zeta Function Number Field Ideal Class Riemann Hypothesis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1994