# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ZetaZero

ZetaZero[k]
represents the k zero of the Riemann zeta function on the critical line.

ZetaZero[k,t]
represents the k zero with imaginary part greater than .

## DetailsDetails

• Mathematical function, suitable for both symbolic and numerical manipulation.
• For positive k, ZetaZero[k] represents the zero of on the critical line that has the k smallest positive imaginary part.
• For negative k, ZetaZero[k] represents zeros with progressively larger negative imaginary parts.
• N[ZetaZero[k]] gives a numerical approximation to the specified zero.
• ZetaZero can be evaluated to arbitrary numerical precision.
• ZetaZero automatically threads over lists.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Find numerically the position of the first zero:

 Out[1]=

Symbolic property:

 Out[1]=