76 citations · 245 across the 41 of their papers we have counts for
45 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…
The bimodal distribution in the derivative of unitary polynomials
David W. Farmer
The derivative of a polynomial with all zeros on the unit circle has the zeros of its derivative on or inside the unit circle. It has been observed that in many cases the zeros of…
The Landscape of L-functions: degree 3 and conductor 1
David W. Farmer, Sally Koutsoliotas, Stefan Lemurell +1
We extend previous lists by numerically computing approximations to many L-functions of degree , conductor , and small spectral parameters. We sketch how previous argumen…
Currently there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
David W. Farmer
We examine published arguments which suggest that the Riemann Hypothesis may not be true. In each case we provide evidence to explain why the claimed argument does not provide a go…
When are the roots of a polynomial real and distinct? A graphical view
David W. Farmer
We prove the classical result, which goes back at least to Fourier, that a polynomial with real coefficients has all zeros real and distinct if and only if the polynomial and also…
Jensen polynomials are not a plausible route to proving the Riemann Hypothesis
David W. Farmer
Recent work on the Jensen polynomials of the Riemann xi-function and its derivatives found a connection to the Hermite polynomials. Those results have been suggested to give eviden…