14 papers
On denominators of consecutive -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
The sequence of -saturated Farey fractions was defined in our previous work by ${\mathscr S}_Q := \{ a/q \in {\mathbb Q} \cap…
Arithmetic Polygons and Sums of Consecutive Squares
Jack Anderson, Amy Woodall, Alexandru Zaharescu
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd , we prove that there…
Twisted aughts of alternating involutions
Raghavendra N. Bhat, Cristian Cobeli, Shuta Iwai +2
Let be the subgroup of generated by the particular involutions that are identical to the identity, except for a single line where and …
On the distribution of -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
We consider the set of Farey fractions of order with the property that there exists a matrix $\left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix}…
Pattern formation Statistics on Fermat Quotients
Cristian Cobeli, Alexandru Zaharescu, Zhuo Zhang
Despite their simple definition as , for and , and their regular arrangement in a Fer…
Angular distribution towards the points of the neighbor-flips modular curve seen by a fast moving observer
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
Let be a fixed non-zero integer. For every and every prime , consider the angles between rays from an observer located at the point on the…