Abstract
We prove a multidimensional extension of Selberg’s central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered process, whose coordinates are all independent and Gaussian.
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Fujii A. (1999). Explicit formulas and oscillations. In: Hejhal, D.A., Friedman, J., Gutzwiller, M.C. and Odlyzko, A.M. (eds) Emerging Applications of Number Theory, pp 219–267. Springer, Heidelberg
Hejhal D.A. (2003). On Euler products and multi-variate Gaussians. C. R. Acad. Sci. Paris Ser. I 337: 223–226
Laurinčikas A. (1996). Limit Theorems for the Riemann Zeta Function. Kluwer, Dordrecht
Revuz D. and Yor M. (1999). Continuous Martingales and Brownian Motion. Springer, Heidelberg
Selberg, A.: Old and new conjectures and results about a class of Dirichlet series. In: Collected Papers, vol. II, pp. 47–63. Springer, Heidelberg (1991)
Tsang K.-M. (1986). Some Ω-theorems for the Riemann zeta-function. Acta Arith. 46: 369–395
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Hughes, C.P., Nikeghbali, A. & Yor, M. An arithmetic model for the total disorder process. Probab. Theory Relat. Fields 141, 47–59 (2008). https://doi.org/10.1007/s00440-007-0079-9
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DOI: https://doi.org/10.1007/s00440-007-0079-9