Vol. 5, No. 2, 2012

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The average order of elements in the multiplicative group of a finite field

Yilan Hu and Carl Pomerance

Vol. 5 (2012), No. 2, 229–236
Abstract

We consider the average multiplicative order of a nonzero element in a finite field and compute the mean of this statistic for all finite fields of a given degree over their prime fields.

Keywords
average multiplicative order, finite field
Mathematical Subject Classification 2010
Primary: 11B05, 11B75
Milestones
Received: 7 December 2011
Revised: 11 January 2012
Accepted: 13 January 2012
Published: 27 January 2013

Communicated by Kenneth S. Berenhaut
Authors
Yilan Hu
55 Maple Hill Road
Thetford Center, VT 05075
United States
Carl Pomerance
Mathematics Department
Kemeny Hall
Dartmouth College
Hanover, NH 03755
United States
www.math.dartmouth.edu/~carlp