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.