Hello and thank you for visiting IMshopping.  What a great question - I have a glass stove top and never thought about using them with copper bottom pans.

While researching this question, I found a lot of information on what can and should not be used on glass top stoves.  It is okay to use copper bottom pans on glass stove tops but these articles feel that they do not provide the best performance and can leave residue that can look like scratches if not cleaned immediately after use.  For best performance they recommend heavy-weight alluminum pots.

Induction and Glass Cooktop - Stovetop Care and Repair

Here is another article is found:

Range - Cookware Used on a Radiant Smooth Glass Cooktop

• Flat Bottom pans are essential for good cooking performance since the bottom of the pan needs to touch the glass for the best heat transfer. Most current brands sold today have flat bottoms. Much older, used cookware and/or thinner cookware will show signs of no longer being flat. Non-flat pans may crack the glass.
  
  
• Use Medium or Heavy-Weight cookware.
• Stainless Steel is highly recommended. A sandwich clad bottom is especially good because it combines the durability and stability of stainless steel with the heat conduction and distribution of aluminum or copper.
  
  
• Heavy-Weight Aluminum cookware is also recommended. It conducts heat faster than other metals and cooks evenly. Aluminum residue sometimes appears as scratches on the cooktop, but these can be removed if cleaned immediately.
  
  
• Copper Bottom pans are also good, but they can leave residues on the cooktop that appear as scratches. These can be removed if cleaned immediately, but do not let a copper bottom pan boil dry. An overheated copper pot will leave a residue that will permanently stain the cooktop.
  
  
• Porcelain/Enamel pans give good performance only if they have a thick, flat bottom. Avoid boiling these pans dry, as porcelain can melt and fuse to the surface.
  
  
• Glass or Ceramic cookware is not recommended. These pans may scratch the surface. Glass is a poor conductor of heat so cooking times will be longer and they may require constant attention during cooking.
  
  
• Stoneware is not recommended. It may scratch the surface and will give poor performance.
  
  
• Cast Iron cookware is not recommended. If the cookware has a burr or rough spot, it will scratch the glass surface. Additionally, it is slow to absorb heat. Once this type of cookware heats up, especially on high heat, it holds an intense amount of heat which is transferred to the cooktop. This can cause the element to shut down as a response to the temperature limiters which indicate surface temperature is too high for cooktop components to handle.
  
  
• Porcelain Coated Cast Iron cookware is okay as long as the cookware is covered completely with porcelain enamel. Caution is recommended when using cast iron cookware that is not completely covered with smooth porcelain enamel, as it may scratch the glass ceramic cooktop. Additionally, if used at hi heat for a long period it will hold heat as described for plain cast iron and could shut down in response to the temperature limiters which indicate surface temperature is too high for cooktop components to handle.
  
  
• Carbon Steel cookware is okay as long as the cookware has a flat bottom and is smooth to avoid scratching.
  
  
• Titanium cookware tested well on ceramic cooktops. Ceramic titanium is a non-stick finish applied to a base metal. We tested one with aluminum as a base metal.

I hope this information has been useful and thank you for visiting IMshopping.

Copper bottom pans are  good, but they can leave residues on the cooktop that appear as scratches. These can be removed if cleaned immediately.