Real analytic Eisenstein series

asked 2020-06-11 22:23:55 +0200

svarot gravatar image

updated 2024-04-15 07:50:12 +0200

FrédéricC gravatar image

I'd to compute values of a certain function in Sage, a kind of a modular form, the so-called real analytic Eisenstein series. Does anybody know how to do it? I could not have found the Sage name for it.

More precisely, I would like to plot the the graph of the real analytic Eisenstein series, their real and imaginary values in a square of the complex plane (variable z) each for a certain value of the parameter s. Thus s is fixed in each of the graphs.

Real analytic Eisenstein series (also this is this their name at wikipedia) are defined for a complex z and a complex s. They are not the Eisenstein series defined for complex z and an integer k. If s is k and an integer, they are connected by the multiple of Im(z)^s. Thus an easy connection, but I'd like to know the value of the series for a complex s. They are modular functions, not holomorphic and connected to theta series.

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I was a bit imprecise , I wanted to plot the graph of these functions, for specific s, more than to compute the values. I edited the question. The problem is that Eisenstein series are incorporated into sage, but they are labelled by a discrete index k. Whereas the real Eisenstein series, I would like to plot, are labelled complex parameter s, or they are functions s.

svarot gravatar imagesvarot ( 2020-06-14 10:27:14 +0200 )edit