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Journal of the London Mathematical Society Advance Access originally published online on May 9, 2008
Journal of the London Mathematical Society 2008 78(2):273-289; doi:10.1112/jlms/jdn022
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© 2008 London Mathematical Society

Extreme values of {zeta}'({rho})

Nathan Ng

Department of Mathematics and Computer Science
University of Lethbridge
4401 University Drive
Lethbridge
Alberta
Canada T1K 3M4

Assuming the Riemann hypothesis, we exhibit large and small values of the derivative of the zeta function evaluated at the non-trivial zeros of the zeta function. These results are proved by applying Soundararajan's resonance method.

This research was funded in part by NSERC and NSF FRG grant DMS 0244660.

2000 Mathematics Subject Classification 11M26 (primary), 11M06 (secondary).

Received April 26, 2007; revised February 8, 2008; published online May 9, 2008.


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