Bootstrap Form PHP not sending

I am trying to get my Bootstrap Form to work. I believe everything is correct in the HTML, but there's something wrong with either the PHP or at my service provider. Does this code look alright? It's a theme from Bootstrap themselves, I just changed the E-mail adress. I have also uploaded it (www.emilseres.com).

<?php
// Check for empty fields
if(empty($_POST['name'])        ||
   empty($_POST['email'])       ||
   empty($_POST['phone'])       ||
   empty($_POST['message']) ||
   !filter_var($_POST['email'],FILTER_VALIDATE_EMAIL))
   {
    echo "No arguments Provided!";
    return false;
   }

$name = $_POST['name'];
$email_address = $_POST['email'];
$phone = $_POST['phone'];
$message = $_POST['message'];

// Create the email and send the message
$to = 'emil.seres.1992@gmail.com'; // Add your email address inbetween the '' replacing yourname@yourdomain.com - This is where the form will send a message to.
$email_subject = "Website Contact Form:  $name";
$email_body = "You have received a new message from your website contact form.\n\n"."Here are the details:\n\nName: $name\n\nEmail: $email_address\n\nPhone: $phone\n\nMessage:\n$message";
$headers = "From: noreply@emilseres.com\n"; // This is the email address the generated message will be from. We recommend using something like noreply@yourdomain.com.
$headers .= "Reply-To: $email_address"; 
mail($to,$email_subject,$email_body,$headers);
return true;            
?>