Explicit bounds for small prime nonresidues
Let $\chi$ be a Dirichlet character modulo a prime~$p$. We give explicit upper bounds on $q_1 0$ such that $q_n\leq Cp^{\frac{1}{4}}(\log p)^{\frac{n+1}{2}}$ whenever $n\leq n_0$ and $p\geq p_0$.
math.NT↗
arXiv subjects
Devon Rhodes
Publications and source records attributed to Devon Rhodes.
On the number of primes for which a polynomial is Eisenstein
Previously Heyman and Shparlinski gave an asymptotic formula with error term for the number of Eisenstein polynomials of fixed degree and bounded height. Let $\psi(f)$ denote the number of primes for which a polynomial $f$ is Eisenstein. We give expressions for the mean and variance of the function $\psi$ for each fixed degree, where the polynomials are ordered according to their height.
math.NT↗