.getElementById() -> this is javascript syntax to get the DOM element having a particular unique Id.
in jQuery it is deferent. You nead to have a selector for that DOM element
Many selectors are there. Here you nead ID SELECTOR. that is: #id
so you need to write like:
$('#ticketCount').submit(function(){
.............................
If you want to submit automatically when the page load use:
window.onload = function(){
$('#ticketCount').trigger("submit");
};