Emails

Okay, in wp-admin\includes\class-wp-upgrader.php, there is a function, send_core_update_notification_email(). This is the function that sends the email notifying the administrator that a new core update is available. In that function is a filter:

if ( ! apply_filters( 'send_core_update_notification_email', $notify, $item ) )
    return false;

$this->send_email( 'manual', $item );
return true;

That basically says, “if $notify is false, then don’t send the email; otherwise, send the email”. So, you just need to tell WordPress that $notify is false. To do that, just add a filter (which you can put in a site functionality Plugin, or a Child Theme:

function designsandcode_prevent_core_update_email( $notify ) {
    __return_false();
}
add_filter( 'send_core_update_notification_email', 'designsandcode_prevent_core_update_email' );

No problem. Happy to help!