Random matrix theory and the derivative of the Riemann zeta function

By C. Hughes, Jon P Keating, Neil 'Connell. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2000

117 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e22797dd88f34d4d08d57a0d1817792336b90c6e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Jon P Keating
2. J. Brian Conrey
3. Kannan Soundararajan
4. Steven M. Gonek
5. C. Hughes
6. N. Snaith
7. M. Shahabi
8. Amir Akbary

In Mathematical Physics

1. Jon P Keating
2. J. Brian Conrey
3. C. Hughes
4. Nathan Ng
5. N. Snaith
6. Steven M. Gonek
7. M. Shahabi
8. Amir Akbary

Citations in the corpus

• Applications of the L‐functions ratios conjectures (2005, background): “1 of Hughes, Keating and O’Connell [23]; since G2(4)/G(7) = 8640 and a(2) = 1/ζ(2), we see that there is agreement between the leading order term of (7.”
• A hybrid Euler-Hadamard product for the Riemann zeta function (2007, methodology): “It can also be used to reproduce other moment results and conjectures, such as those given by Gonek [7] and by Hughes, Keating, and O’Connell [ 10 ] concerning derivatives of the Riemann zeta function at the zeros of the zeta function.”
• LIMITING DISTRIBUTIONS OF THE CLASSICAL ERROR TERMS OF PRIME NUMBER THEORY (2013, background): “Hence, assuming the generalized Riemann hypothesis forL(s, π), Corollary 1.3(b) implies that E1(y, π) has a limiting distribution.”