Using AJAX with Forms

I am attempting to validate and submit a form using AJAX in WordPress, however, the response that I am getting is 0. According to the codex, this would seem to indicate that admin-ajax is unable to find the functions that I defined.

What am I doing wrong?

Code (Simplified for Demonstration Purposes)

<script type="text/javascript">

jQuery(function()
{
    jQuery(document).on('click', '#test-button', function()
    {
        var name = jQuery("#name").val();
        var AdminAJAX = <?php echo json_encode(admin_url('admin-ajax.php')); ?>;
        
        var ajaxparams = {
            action: 'jp_ajax_request',
            name: name
            };

        jQuery.post( AdminAJAX, ajaxparams, function( response )
        {
            alert(response);
        });
    }
}
</script>

<?php
add_action( 'wp_ajax_jp_ajax_request', 'jp_ajax_process');
add_action( 'wp_ajax_nopriv_jp_ajax_request', 'jp_ajax_process');

function jp_ajax_process()
{
    echo 'ajax response';
    die();
}
?>

<form action="">
    <input type="text" id="name">
    <button id="test-button">Submit</button>
</form>