This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 NumberTheory`Ramanujan` The Riemann function is the simplest of all Dirichlet series. Ramanujan studied the Dirichlet series where the are the coefficients of in the series expansion Just as there is the Riemann hypothesis that all of the nontrivial zeros of the lie on the critical line , there is a conjecture due to Ramanujan that all of the nontrivial zeros of lie on the critical line . The function satisfies the functional equation Just as can be split into where is RiemannSiegelZ and is RiemannSiegelTheta, can split into where and Functions related to the Ramanujan -Dirichlet series. The Ramanujan -Dirichlet series is rather difficult to evaluate, especially far up the critical line . It is only within the last few years that even a few of the zeros have been verified to lie on the critical line. This package does not provide any great new method to help with this effort, but it does use the fastest methods known. This loads the package. In[1]:= <