4 papers
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…
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 posit…
Multiplicity one for -functions and applications
David W. Farmer, Ameya Pitale, Nathan C. Ryan +1
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other…
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…