Database of the zeros of the Riemann zeta function#

The main access function to the database of the zeros of the Riemann zeta function is zeta_zeros(). In order to use zeta_zeros(), you need to install the optional database_odlyzko_zeta package:

sage -i database_odlyzko_zeta

AUTHORS:

  • William Stein: initial version

  • Jeroen Demeyer (2015-01-20): converted database_odlyzko_zeta to new-style package

sage.databases.odlyzko.zeta_zeros()[source]#

List of the imaginary parts of the first 2,001,052 zeros of the Riemann zeta function, accurate to within 4e-9.

REFERENCES:

EXAMPLES:

The following example shows the imaginary part of the 13th nontrivial zero of the Riemann zeta function:

sage: # optional - database_odlyzko_zeta
sage: zz = zeta_zeros()
sage: zz[12]
59.347044003
sage: len(zz)
2001052

>>> from sage.all import *
>>> # optional - database_odlyzko_zeta
>>> zz = zeta_zeros()
>>> zz[Integer(12)]
59.347044003
>>> len(zz)
2001052