5 papers
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…
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…
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*} π(x+y)\leqslant π(x)+π(y) \end{align*} fo…
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…
Fermat quotients and the Ankeny-Artin-Chowla conjecture
Nic Fellini, M. Ram Murty
In this article, we present streamlined proofs of results of Ankeny, Artin, and Chowla concerning the fundamental unit of the real quadratic field for primes…