I've seen equally good arguments for and against using "is" for this sentence.
The pair of polynomials (f,g) is/are related by the reciprocity law.
Which verb is used correctly?
You should use the singular, because it refers to "Pair" and not to "polynomials". The pair in this case is one, so "is".
If it was "three pairs of polynomials...", for example, then you would have used "are".
If the mathematical statement is about the two objects in the pair then "are" is appropriate, however if it is about the pair as a mathematical object of itself then "is" is in place. Thus "The pair of polynomials (f,g) are related by the reciprocity law" but "The pair of polynomials (f,g) is equal to the pair (h,q)".