4 papers
math.NT2026
Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
Nic Fellini, M. Ram Murty
For a prime , let \[ \varepsilon = \frac{1}{2}\left( t + u\sqrt{p}\right) \] be the fundamental unit of the real quadratic field . In…
math.NT2025
A note on arithmetic congruences
Nic Fellini
By analyzing the coefficients of the power series defining the Kubota--Leopoldt -adic -function associated to the non-trivial character of a real quadratic field, we prove a…
math.NT2025
On the Second Hardy-Littlewood Conjecture
Bittu Chahal, Ertan Elma, Nic Fellini +2
The second Hardy-Littlewood conjecture asserts that the prime counting function satisfies the subadditive inequality \begin{align*} Ï(x+y)\leqslant Ï(x)+Ï(y) \end{align*…
math.NT2024
Congruence relations of Ankeny$\unicode{x2013}$Artin$\unicode{x2013}$Chowla type for real quadratic fields
Nic Fellini
In 1951, Ankeny, Artin, and Chowla published a brief note containing four congruence relations involving the class number of for positive squarefree integers…