Number Theory I pp 208-274 | Cite as

# Zeta Functions and Modular Forms

Chapter

## Abstract

Let *X* be a scheme of finite type over Spec ℤ (see §1 of Chapter 3). Then the closed points *x ∈ X* are those which satisfy the condition that the corresponding residue field *R*(*x*) is finite. The cardinality of *R(x)* is called the norm of *x* and is denoted by N(*x*). The set of all closed points of *X* is denoted by *̄X*. For the moment we shall think of this as a discrete topological space.

## Keywords

Zeta Function Modular Form Elliptic Curve Eisenstein Series Cusp Form
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1995