Uniform asymptotics of the coefficients of unitary moment polynomials
2010 ◽
Vol 467
(2128)
◽
pp. 1073-1100
◽
Keyword(s):
Keating and Snaith showed that the 2 k th absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree k 2 . In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in an explicit form. Numerical data to support these calculations are presented. Some apparent connections between the random matrix theory and the Riemann zeta function are discussed.
2004 ◽
Vol 109
(2)
◽
pp. 240-265
◽
Keyword(s):
Generalized Wirtinger inequalities, random matrix theory, and the zeros of the Riemann zeta-function
2002 ◽
Vol 97
(2)
◽
pp. 397-409
◽
Keyword(s):
2008 ◽
Vol 128
(10)
◽
pp. 2836-2851
◽
Keyword(s):
2000 ◽
Vol 456
(2003)
◽
pp. 2611-2627
◽
Keyword(s):
2016 ◽
Vol 472
(2194)
◽
pp. 20160548
◽
2003 ◽
Vol 36
(12)
◽
pp. 2907-2917
◽
2014 ◽
Vol 157
(3)
◽
pp. 425-442
◽