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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

Asymptotic estimation of $ \xi^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades


Author: Mark W. Coffey
Journal: Math. Comp. 78 (2009), 1147-1154
MSC (2000): Primary 11M06, 30D15
Published electronically: June 20, 2008
MathSciNet review: 2476576
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Abstract: We verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann xi function at $ s=1/2$. We give two separate proofs of this result, with the more general method not restricted to $ s=1/2$. We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.


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Additional Information

Mark W. Coffey
Affiliation: Department of Physics, Colorado School of Mines, Golden, Colorado 80401

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02167-4
PII: S 0025-5718(08)02167-4
Keywords: Xi function, derivatives of the Riemann $\xi $ function, asymptotic estimation, Tur\'{a}n differences.
Received by editor(s): March 17, 2006
Received by editor(s) in revised form: April 24, 2008
Published electronically: June 20, 2008
Article copyright: © Copyright 2008 by the author