On a class of lacunary almost Newman polynomials modulo p and density theorems

Denys Dutykh, Jean-Louis Verger-Gaugry

The reduction modulo $p$ of a family of lacunary integer polynomials, associated with the dynamical zeta function ${\zeta }_{\beta }(z)$ of the $\beta$-shift, for $\beta >1$ close to one, is investigate…