What is the difference between via or through and when would you use one over the other? Would you say, for example, reply through e-mail or reply via e-mail? They seem to be used as some sort of synonyms.

Also, could you please let me know which one of the following is correct: the two elements related through a mathematical function, the two elements related via a mathematical function or the two elements related by a mathematical function?

I look forward to hearing from you soon.

Thanks in advance.

George