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Abstract We obtain conditional upper bounds for negative discrete moments of the derivative of the Riemann zeta‐function averaged over a subfamily of zeros of the zeta function that is expected to be arbitrarily close to full density inside the set of all zeros. For , our bounds for the ‐th moments are expected to be almost optimal. Assuming a conjecture about the maximum size of the argument of the zeta function on the critical line, we obtain upper bounds for these negative moments of the same strength while summing over a larger subfamily of zeta zeros.
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Sharp Rosenthal‐type inequalities for mixtures and log‐concave variables
Abstract We obtain Rosenthal‐type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremizers in log‐concave settings when the moments of summands are individually constrained.
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- Award ID(s):
- 1955175
- PAR ID:
- 10418083
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 55
- Issue:
- 3
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- p. 1222-1239
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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