4 papers
Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
Natasha Dhiman, Habiba Kadiri, Emily Quesada-Herrera
We show an explicit version of the Van der Corput truncated Poisson summation formula (B-process). By using refined explicit exponential sum estimates, this improves the error term…
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 the number variance of zeta zeros and a conjecture of Berry
Meghann Moriah Lugar, Micah B. Milinovich, Emily Quesada-Herrera
Assuming the Riemann hypothesis, we prove estimates for the variance of the real and imaginary part of the logarithm of the Riemann zeta-function in short intervals. We give three…
Generalized sign Fourier uncertainty
Emanuel Carneiro, Emily Quesada-Herrera
We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gonça…