Cleaning White Spots on Black Cooktop?

If it is a glass top, and has the solid burner, there is a product that is almost like a black paste shoe polish made to clean the burners. I forget the name of it. But, years ago I used to get it at sears (where my cook top came from). I still have that unit in a rental house and it worked very well. Check in some appliance stores.

Try the Mr Clean Magic Eraser.