M. Harm

collaborators

4 papers

math.NT2026

The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem

Michael Harm, Daniel R. Johnston

We prove new results on the additive theory of reversed primes $p$ ; that is, primes $p$ which are written backwards in a fixed base $b \geq 2$ . In particular, we stu…

math.NT2026

On the Goldbach problem with restricted primes

Michael Harm

Let $N$ be a sufficiently large, odd integer. We prove an asymptotic formula for the number of representations of $N$ as the sum of three primes, one of which is smaller than a giv…

math.NT2026

Refinements for primes in short arithmetic progressions

Michael Harm

Given a zero-free region and an averaged zero-density estimate over all Dirichlet $L$ -functions modulo $q \in N$ , we refine the error terms of the prime number theorem in al…

math.NT2026

Distribution of solutions to systems of congruences in balls

Michael Harm

Let $G_{1}, \dots, G_{n} \in F_{p} [X_{1}, \dots, X_{m}]$ be $n$ polynomials in $m$ variables over the finite field $F_{p}$ of $p$ elements. For any sufficiently large prime $p$ a…