  We analize the Berry-Keating model and the Sierra and Rodr\'iguez-Laguna
Hamiltonian within the polymeric quantization formalism. By using the polymer
representation, we obtain for both models, the associated polymeric quantum
Hamiltonians and the corresponding stationary wave functions. The
self-adjointness condition provide a proper domain for the Hamiltonian operator
and the energy spectrum, which turned out to be dependent on an introduced
scale parameter. By performing a counting of semiclassical states, we prove
that the polymer representation reproduces the smooth part of the Riemann-von
Mangoldt formula, and introduces a correction depending on the energy and the
scale parameter, which resembles the fluctuation behavior of the Riemann zeros.
