The Expected Number of Roots over The Field of <i>p</i>-adic Numbers
The Expected Number of Roots over The Field of <i>p</i>-adic Numbers
Abstract We study the roots of a random polynomial over the field of $p$-adic numbers. For a random monic polynomial with i.i.d. coefficients in ${\mathbb{Z}}_p$, we obtain an estimate for the expected number of roots of this polynomial. In particular, if the coefficients take the values $\pm 1$ with equal …