Asymptotic estimation of 𝜉⁽²ⁿ⁾(1/2): On a conjecture of Farmer and Rhoades

Coffey, Mark

doi:10.1090/S0025-5718-08-02167-4

Asymptotic estimation of $\xi ^{(2n)}(1/2)$: On a conjecture of Farmer and Rhoades
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by Mark W. Coffey PDF

Math. Comp. 78 (2009), 1147-1154

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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