13.7 Tables of zeros of the Riemann-Zeta function

Module: sage.databases.odlyzko

Tables of zeros of the Riemann-Zeta function.

Module-level Functions

zeta_zeros( )

List of the imaginary parts of the first 100,000 nontrivial zeros of the Riemann zeta function. Andrew Odlyzko computed these to precision within $3\cdot 10^{-9}$ .

In order to use zeta_zeros(), you will need to install the optional Odlyzko database package: sage -i database_odlyzko_zeta. You can see a list of all available optional packages with sage -optional.

REFERENCES: http://www.dtc.umn.edu/ odlyzko/zeta_tables/

The following example prints the imaginary part of the 13th nontrivial zero of the Riemann zeta function. Note that only the first 9 digits after the decimal come from the database. Subsequent digits are the result of the inherent imprecision of a binary representation of decimal numbers.

sage: zz = zeta_zeros() # optional
sage: zz[12]            # optional
59.347044003000001

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