49 citations · 237 across the 16 of their papers we have counts for
17 papers
A heuristic for discrete mean values of the derivative of the Riemann zeta function
Christopher Hughes, Greg Martin, Andrew Pearce-Crump
Shanks conjectured that , where ranges over non-trivial zeros of the Riemann zeta function, is real and positive in the mean. We present a history of this problem, incl…
A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
We show that the th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for odd/even, respecti…
Probabilistic models for Gram's Law
Cătălin Hanga, Christopher Hughes
Gram's Law describes a pattern that frequently occurs in the distribution of the non-trivial zeros of the Riemann zeta function along the critical line. Whenever Gram's Law holds t…
The effect of repeated differentiation on -functions
Jos Gunns, Christopher Hughes
We show that under repeated differentiation, the zeros of the Selberg -function become more evenly spaced out, but with some scaling towards the origin. We do this by showing th…
On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices
Yacine Barhoumi, Chris Hughes, Joseph Najnudel +1
We show that almost all the zeros of any finite linear combination of independent characteristic polynomials of random unitary matrices lie on the unit circle. This result is the r…
Random permutation matrices under the generalized Ewens measure
Christopher Hughes, Joseph Najnudel, Ashkan Nikeghbali +1
We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition,…