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I would like to apply for the Crossgrade version, but I have no idea about the serial number. [STEINBERG]

The Apple/Logic does not have a serial number but you're required the receipt email from Apple when you purchase the product.

If you have no idea about the receipt email, please send us the screenshot of your purchase history that you can view as below.
 
■To view your purchase history on iPhone
Settings→Account Name→"iTunes and App Store"→Tap your Apple ID
Display your Apple ID and enter your password to sign in.
Tap "Purchase History", select year and month you purchased the Apple/Logic to display the screen you're required to capture and send instead of the receipt email.
 
■To view from iTunes
Menu→Account→select "View My Account"
Sign in with your Apple ID and click on "View My Account"
Display "Purchase History" on the bottom of the page and "See All" to display your older purchase history as well.

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