Department of Mathematics


  •  The ranges of some familiar arithmetic functions
  •  10/13/2016
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Carl Pomerance, Dartmouth College

We consider 4 functions from elementary number theory: sigma (the sum-of-divisors function), phi (Euler's function), lambda (Carmichael's universal exponent function), and s (the sum-of-proper-divisors function). In particular we discuss the distribution of the values of these functions, and coincidences of values. Most of the problems considered have a fairly long history, some over 80 years. We report on recent progress. (Various parts of this work are joint with Kevin Ford, Florian Luca, Paul Pollack, and others.)



Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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