# Numerical methods for Eisenstein series

Are there any existing numerical libraries for Eisenstein series? In particular I am interested in calculating values of parabolic Eisenstein series on $SL(n,\mathbb Z) \setminus GL(n,\mathbb R) / (O(n,\mathbb R),\mathbb R^{\times})$. If no such libraries exist, might there be a formulation of the series which is more suitable for numerical computations? Ultimately I would like to be able to numerically calculate integrals whose integrand contain such Eisenstein series, which is why I am in search of more efficient methods.

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There is apparently a set of functions for Mathematica for doing some computations for automorphic forms on $GL(n,\mathbb R)$ called GL(n)pack (math.waikato.ac.nz/~kab/glnpack.html). You might also look at Goldfeld's book "Automorphic Forms and L-Functions for the Group $GL(n,\mathbb R)$", which mentions GL(n)pack. I've never used it, so I'm leaving this as a comment. –  B R Sep 29 '12 at 4:49
Thanks for your comment. GL(n)pack has various tools for calculating the summands of the series, the Fourier coefficients, and the factors in the functional equation, but does not have a tool to approximate the values of the series. Goldfeld's book is one of my main references, and as far as I know it does not contain any such numerical methods. –  R. Rosenbaum Sep 29 '12 at 14:07
Oh, well! Hopefully someone else knows something. By the way, are answers to your question known for GL(2)? Also, if you feel comfortable, it would be interesting to see an example of what you want to accomplish. –  B R Sep 29 '12 at 16:13