83 citations · 1k across the 45 of their papers we have counts for
11 papers · 1 filter
Hilbert spaces and low-lying zeros of L-functions
Emanuel Carneiro, Andrés Chirre, Micah B. Milinovich
Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of -functions in a…
On Montgomery's pair correlation conjecture: a tale of three integrals
Emanuel Carneiro, Vorrapan Chandee, Andrés Chirre +1
We study three integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. The first is the integral of Montgomery's function in bounded interval…
Optimality for the two-parameter quadratic sieve
Emanuel Carneiro, Andrés Chirre, Harald Andrés Helfgott +1
We study the two-parameter quadratic sieve for a general test function. We prove, under some very general assumptions, that the function considered by Barban and Vehov [BV68] and G…
Bandlimited approximations and estimates for the Riemann zeta-function
Emanuel Carneiro, Andrés Chirre, Micah B. Milinovich
In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Ri…
Fourier optimization and prime gaps
Emanuel Carneiro, Micah B. Milinovich, Kannan Soundararajan
We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest pos…
Bounding on the Riemann hypothesis
Emanuel Carneiro, Andrés Chirre
Let be the argument of the Riemann zeta-function at the point . For and define its iterates \begin{equation…