ZetaZero

ZetaZero[k]

represents the k^(th) zero of the Riemann zeta function on the critical line.

ZetaZero[k,t]

represents the k^(th) zero with imaginary part greater than t.

Details

  • 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^(th) 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.

Examples

open allclose all

Basic Examples  (2)

Find numerically the position of the first zero:

In[1]:=
Click for copyable input
Out[1]=

Symbolic property:

In[1]:=
Click for copyable input
Out[1]=

Scope  (3)

Generalizations & Extensions  (1)

Applications  (4)

Properties & Relations  (1)

Possible Issues  (1)

See Also

Zeta  RiemannSiegelZ  PrimePi  RiemannR

Tutorials

Introduced in 2007
(6.0)