Asymptotic estimation of $\xi ^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades
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- by Mark W. Coffey;
- Math. Comp. 78 (2009), 1147-1154
- DOI: https://doi.org/10.1090/S0025-5718-08-02167-4
- Published electronically: June 20, 2008
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.References
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Bibliographic Information
- Mark W. Coffey
- Affiliation: Department of Physics, Colorado School of Mines, Golden, Colorado 80401
- Received by editor(s): March 17, 2006
- Received by editor(s) in revised form: April 24, 2008
- Published electronically: June 20, 2008
- © Copyright 2008 by the author
- Journal: Math. Comp. 78 (2009), 1147-1154
- MSC (2000): Primary 11M06, 30D15
- DOI: https://doi.org/10.1090/S0025-5718-08-02167-4
- MathSciNet review: 2476576