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math-ph2018★ 21 cited
A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
Estelle Basor, Pavel Bleher, Robert Buckingham +4
We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the sigma-Painleve V equatio…
math.NT2018★ 9 cited
Some multidimensional integrals in number theory and connections with the Painlevé V equation
Estelle Basor, Fan Ge, Michael O. Rubinstein
We study piecewise polynomial functions that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the…