5 papers
The shifted convolution problem in function fields
Alexandra Florea, Matilde Lalín, Amita Malik +1
We study the shifted convolution problem for the divisor function in function fields in the large degree limit, that is, the average value of where runs over moni…
Hilbert transforms and the equidistribution of zeros of polynomials
Emanuel Carneiro, Mithun Kumar Das, Alexandra Florea +5
We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upo…
Equidistribution of with a Chebotarev condition and applications to extremal primes
Amita Malik, Neha Prabhu
We establish a joint distribution result concerning the fractional part of for , where is a prime satisfying a Chebotarev condition in a fixed finite…
Extremal primes of elliptic curves without complex multiplication
C. David, A. Gafni, A. Malik +2
Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to th…
Spatial Statistics of Apollonian Gaskets
Weiru Chen, Mo Jiao, Calvin Kessler +2
Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the pair correlation…