2 papers
math.NT2025
Refinements of Artin's primitive root conjecture
Leo Goldmakher, Greg Martin, Paul Péringuey
A famous conjecture of Artin asserts that any integer that is neither nor a square should be a primitive root (mod ) for a positive proportion of primes . Moreover,…
math.NT2024
A converse to a theorem of Gauss on Gauss sums
Jonathan W. Bober, Leo Goldmakher
In this note we prove (under mild hypotheses) that is a nontrivial character of if and only if the Fourier transform of has magnitude 1 somewhere in $\mathbb…