30 citations · 110 across the 33 of their papers we have counts for
7 papers · 2 filters
Correlation of arithmetic functions over
Ofir Gorodetsky, Will Sawin
For a fixed polynomial , we study the number of polynomials of degree over such that and are both irreducible, an -analogue of th…
Chebotarev density theorem in short intervals for extensions of
Lior Bary-Soroker, Ofir Gorodetsky, Taelin Karidi +1
An old open problem in number theory is whether Chebotarev density theorem holds in short intervals. More precisely, given a Galois extension of with Galois group…
The variance of the number of sums of two squares in in short intervals
Ofir Gorodetsky, Brad Rodgers
Consider the number of integers in a short interval that can be represented as a sum of two squares. What is an estimate for the variance of these counts over random short interval…
Mean values of arithmetic functions in short intervals and in arithmetic progressions in the large-degree limit
Ofir Gorodetsky
A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progressio…
Irreducible polynomials over with three prescribed coefficients
Ofir Gorodetsky
For any positive integers and , we prove that the number of monic irreducible polynomials of degree over in which the coefficients of $T^{…
q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
Ofir Gorodetsky
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding -supercongruence. Similar -supercongruences are established for binomial coeffi…