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math.NT2025
Oscillation results for the summatory functions of fake mu's
Greg Martin, Chi Hoi Yip
Mossinghoff, Trudgian, and the first author~\cite{MMT23} recently introduced a family of arithmetic functions called ``fake 's'', which are multiplicative functions for which t…
math.NT2024
An annotated bibliography for comparative prime number theory
Greg Martin, Pu Justin Scarfy Yang, Aram Bahrini +9
The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We…
math.NT2024
Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs
Greg Martin, Chi Hoi Yip
We derive an asymptotic formula for the number of solutions in a given subfield to certain system of equations over finite fields. As an application, we construct new families of m…