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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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
Keywords
- Total disorder process
- Convergence in distribution
- Central limit theorem
- Riemann zeta function
Mathematics Subject Classification (2000)
- 60F05
- 60G15
- 11M06