49 citations · 98 across the 5 of their papers we have counts for
7 papers
Short mollifiers of the Riemann zeta-function
J. Brian Conrey, David W. Farmer, Chung-Hang Kwan +2
We apply the calculus of variations to construct a new sequence of linear combinations of derivatives of the Riemann -function adapted to Levinson's method, which yield a positi…
On -gaps between zeros of the Riemann zeta-function
J. B. Conrey, C. L. Turnage-Butterbaugh
Under the Riemann Hypothesis, we prove for any natural number there exist infinitely many large natural numbers such that and…
An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion
Sandro Bettin, J. Brian Conrey, David W. Farmer
We give a conditional result on the constant in the Báez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothes…
The nontrivial zeros of period polynomials of modular forms lie on the unit circle
J. Brian Conrey, David Farmer, Ozlem Imamoglu
We show that all but 5 of the zeros of the period polynomial associated to a Hecke cusp form are on the unit circle.
Period functions and cotangent sums
Sandro Bettin, Brian Conrey
We investigate the period function of $\sum_{n=1}^\inftyσ_a(n)\e{nz}$, showing it can be analytically continued to and studying its Taylor series. We use these results…
More than 41% of the zeros of the zeta function are on the critical line
Hung Bui, Brian Conrey, Matthew Young
We prove that more than 41% of the zeros of the zeta function are on the critical line.
Correlations of eigenvalues and Riemann zeros
J. B. Conrey, N. C. Snaith
We present a new approach to obtaining the lower order terms for -correlation of the zeros of the Riemann zeta function. Our approach is based on the `ratios conjecture' of Conr…