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Maass cusp forms for GSp(4)

Currently in the LMFDB, we have data on L-functions associated to Maass cusp forms for GSp(4) of level 1. These satisfy a functional equation with \(\Gamma\)-factors \[\begin{aligned}\Gamma_\R(s + i \mu_1)\Gamma_\R(s + i \mu_2)\Gamma_\R(s - i \mu_1)\Gamma_\R(s - i \mu_2)\end{aligned}\] with \(0 \le \mu_2 \le \mu_1\).

L-functions of conductor 1

The dots in the plot correspond to L-functions with \((\mu_1,\mu_2)\) in the \(\Gamma\)-factors, colored according to the sign of the functional equation (blue indicates \(\epsilon=1\)). Click on any of the dots for detailed information about the L-function.


Maass cusp forms for GL(4)

Currently in the LMFDB, we have data on L-functions associated to Maass cusp forms for GL(4) of level 1. These satisfy a functional equation with \(\Gamma\)-factors \[\begin{aligned}\Gamma_\R(s + i \mu_1)\Gamma_\R(s + i \mu_2)\Gamma_\R(s - i \mu_3)\Gamma_\R(s - i \mu_4)\end{aligned}\] where \(\mu_1 + \mu_2 = \mu_3 + \mu_4\).

L-functions of conductor 1

The dots in the plot correspond to L-functions with \((\mu_1,\mu_2)\) in the \(\Gamma\)-factors, colored according to the sign of the functional equation (blue indicates \(\epsilon=1\)). Click on any of the dots for detailed information about the L-function.