6 papers
Littlewood's estimates for -functions in the hyperelliptic ensemble
Emanuel Carneiro, Pranendu Darbar, Mithun Kumar Das +2
We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet -functions over function fields. In…
Effective equidistribution of Galois orbits for mildly regular test functions
Emanuel Carneiro, Mithun Kumar Das
In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N…
Sign uncertainty and de Branges spaces
Emanuel Carneiro, Tolibjon Ismoilov, Antonio Pedro Ramos
We investigate here the sign uncertainty phenomenon for bandlimited functions, with a competing condition given by integration with respect to a general measure. Our main result pr…
Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression
Emanuel Carneiro, Micah B. Milinovich, Emily Quesada-Herrera +1
By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least qu…
On Littlewood's estimate for the modulus of the zeta function on the critical line
Emanuel Carneiro, Micah B. Milinovich
Inspired by a result of Soundararajan, assuming the Riemann hypothesis (RH), we prove a new inequality for the logarithm of the modulus of the Riemann zeta-function on the critical…
Fourier optimization and Montgomery's pair correlation conjecture
Emanuel Carneiro, Micah B. Milinovich, Antonio Pedro Ramos
Assuming the Riemann hypothesis, we improve the current upper and lower bounds for the average value of Montgomery's function over long intervals by means of a Fourier op…