ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 14 Jun 2020 03:27:14 -0500Real analytic Eisenstein serieshttps://ask.sagemath.org/question/51911/real-analytic-eisenstein-series/I'd to compute values of a certain function in Sage, a kind of a modular form, the so-called [real analytic Eisenstein series](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/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.Thu, 11 Jun 2020 13:40:09 -0500https://ask.sagemath.org/question/51911/real-analytic-eisenstein-series/Comment by svarot for <p>I'd to compute values of a certain function in Sage, a kind of a modular form, the so-called <a href="https://en.wikipedia.org/wiki/Real_analytic_Eisenstein_series">real analytic Eisenstein series</a>. Does anybody know how to do it? I could not have found the Sage name for it.</p>
<p>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. </p>
<p>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 <a href="https://en.wikipedia.org/wiki/Eisenstein_series">Eisenstein series</a> 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.</p>
https://ask.sagemath.org/question/51911/real-analytic-eisenstein-series/?comment=51960#post-id-51960I 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.Sun, 14 Jun 2020 03:27:14 -0500https://ask.sagemath.org/question/51911/real-analytic-eisenstein-series/?comment=51960#post-id-51960