Abstract : We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this identity can be generalized and derive an explicit formula for the sums.
https://hal.inria.fr/hal-00958949
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Johannes Grassberger, Günther Hörmann. A note on representations of the finite Heisenberg group and sums of greatest common divisors. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, 4 (2), pp.91-100. 〈hal-00958949〉
