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Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta Function

โœ Scribed by Fyodorov, Yan; Hiary, Ghaith; Keating, Jonathan


Book ID
111642872
Publisher
The American Physical Society
Year
2012
Tongue
English
Weight
161 KB
Volume
108
Category
Article
ISSN
0031-9007

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An explicit formula of Atkinson type for
โœ Hideaki Ishikawa; Kohji Matsumoto ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› SP Versita ๐ŸŒ English โš– 413 KB

We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first autho