{% extends 'homepage.html' %}

{% block content %}
        <h1> {{ title }} </h1>

{% if info.degree==1 %}
<div>There are two types of degree 1 L-functions: the Riemann zeta function and
Dirichlet L-functions associatedto a primitive Dirichlet character.</div>

[[
the rest of this page should be ab expansion of what is currently available at

http://l-functions.org/Lfunction/Character/Dirichlet

]]

{% endif %}

{% if info.degree==2 %}
<div>There are two known types of primitive degree 2 L-functions:</div>
<p>
<div>$L(s, f)$: the L-function of a holomorphic newform in $S_k(\Gamma_0(N))$</div>
<p>
<div>$L(s, f)$: the L-function of a Maass cusp form on  $\Gamma_0(N)$</div>

[[ page under construction]]
{% endif %}

{% if info.degree==3 %}
<div>The known types of primitive degree 4 L-functions are:</div>
<p>
<div>$L(s, f, \mathrm{sym}^2)$: the symmetric square of a degree 2 L-function</div>
 <p>
<div>$L(s,f)$: standard L-function of a cusp form on GL(3)</div>


<h2>Available Examples:</h2>

<h3>Maass cusp forms on SL(3,Z)</h3>

Here we want to include the material that is currently in the file:

plotOfEigenvalues.html

{% endif %}
 
{% if info.degree==4 %}
<div>The known types of primitive degree 4 L-functions are:</div>
<p>
<div>$L(s, f, \mathrm{sym}^3)$: the symmetric cube L-function of a cusp form on GL(2)</div>
        <p>

        <div>$L(s, f, \mathrm{sym}^3)$: the symmetric cube L-function of a cusp form on GL(2)</div>
        <p>
	<div>$L(s, F, \mathrm{spin})$: spin L-function of a Siegel modular form on GSp(4) (genus 2)</div>
	<p>
	<div>$L(s,f)$: standard L-function of a cusp form on the Picard group SL(2,Z[i])</div>
	<p>
	<div>$L(s,f)$: standard L-function of a cusp form on Sp(4)</div>

	<p>
	<div>$L(s,f)$: standard L-function of a cusp form on GL(4)</div>
	<p>
	<div>$L(s,E)$: L-function of an elliptic curve over a quadratic field</div>
	<p>
	<div>$L(s,f)$: standard L-function of a Hilbert modular form on GL(2) over a real quadratic field</div>
        <p>

<h2>Available Examples:</h2>

<h3>Maass cusp forms on Sp(4,Z)</h3>
<div>These satisfy a functional equation with $\Gamma$-factors
\begin{equation}
\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{equation}
with $0 \le \mu_2 \le \mu_1$.
</div>
<div>The dots in the plot correspond to $(\mu_1,\mu_2)$ for Sp(4,Z) L-functions
which have been found by a computer search.</div>
<embed src="http://www.aimath.org/~farmer/print/Sp4.svg" width="470" height="330">
<br>
<h3>Maass cusp forms on SL(4,Z)</h3>
<div>These satisfy a functional equation with $\Gamma$-factors
\begin{equation}
\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{equation}
where $\mu_1 + \mu_2 = \mu_3 + \mu_4$.
</div>
<div>The dots in the plot correspond to $(\mu_1,\mu_2)$ for SL(4,Z) L-functions
which have been found by a computer search.</div>
<embed src="http://www.aimath.org/~farmer/print/SL4.svg" width="520" height="360">
{% endif %}
 
{% endblock %}