Prof. Sneha Chaubey (IIIT Delhi) will be visiting IIT Bombay on Monday,
28th July. She will deliver a number theory seminar on Monday, 28th July
at 4pm in the Ramanujan Hall. Further details below:
Title: On the distribution of polynomial Farey fractions
Abstract: The notion of classical visibility from the origin has been
generalised by viewing lattice points through curved lines of sight. This
generalisation motivates us to define polynomial Farey fractions. For a
positive integer $Q$, and polynomial $P(x)\in\mathbb{Z}[X]$ with $P(0)=0$,
we define polynomial Farey fractions as
\[\mathcal{F}_{Q,P}:=\left\{\frac{a}{q}: 1\leq a\leq q\leq Q,\ \gcd
(P(a),q)=1\right\}.\] The classical Farey fractions are obtained by
considering $P(x)=x$. In this talk, we will look at the global and local
distribution of the sequence of polynomial Farey fractions via discrepancy
and pair correlation measure, respectively. In particular, restricting the
polynomial Farey denominators to certain subsets of primes yields explicit
estimates of the pair correlation measure.