Is there a convenient way to work with Siegel modular forms in Mathematica? I am interested in doing analytic computations using the $\chi_{10}(\Omega)$ Siegel modular form, where $\Omega$ is the $2\times 2$ matrix $$ \begin{pmatrix} \rho & v \\ v & \sigma \end{pmatrix}. $$ I am aware that Mathematica has built-in functions for Siegel Theta functions, but I am not sure if these can be used to get $\chi_{10}$. Are there any packages or functions that are specifically designed for working with these forms?
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- 1$\begingroup$ I would encourage you to add a computational-math tag (computer-algebra? I'm not sure what's appropriate). Without it, the users most familiar with CAS's might not see your question. Also, have you tried asking at MathematicaSE? $\endgroup$LSpice– LSpice2023-01-16 18:25:16 +00:00Commented Jan 16, 2023 at 18:25
- 1$\begingroup$ Thanks, I have also posted the question on MathematicaSE. $\endgroup$Holomaniac– Holomaniac2023-01-16 20:10:18 +00:00Commented Jan 16, 2023 at 20:10
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1 Answer
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You might want to check out the documentation on Siegel Modular Forms by Yuen, Poor, Shurman, and King. It provides a variety of Mathematica and Maple notebooks.
