Multiplicative Structure of Values of the Euler Function

MOspace/Manakin Repository

Breadcrumbs Navigation

Multiplicative Structure of Values of the Euler Function

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/10645

[-] show simple item record

dc.contributor.author Banks, William David, 1964-
dc.contributor.author Friedlander, J. B. (John B.)
dc.contributor.author Pomerance, Carl
dc.contributor.author Shparlinski, Igor E.
dc.date.accessioned 2011-05-05T17:29:19Z
dc.date.available 2011-05-05T17:29:19Z
dc.date.issued 0000
dc.identifier.uri http://hdl.handle.net/10355/10645
dc.description This is a preprint of a book chapter published in High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS (2004). © American Mathematical Society. en_US
dc.description.abstract We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has a certain “smoothing” effect on its integer arguments, our results show that, in fact, most values produced by the Euler function are not smooth. We apply our results to study the distribution of “strong primes”, which are commonly encountered in cryptography. We also consider the problem of obtaining upper and lower bounds for the number of positive integers n ≤ x for which the value of the Euler function φ (n) is a perfect square and also for the number of n ≤ x such that φ (n) is squarefull. We give similar bounds for the Carmichael function λ (n). en_US
dc.language.iso en_US en_US
dc.relation.ispartof Mathematics publications (MU) en
dc.source.uri http://www.math.missouri.edu/~bbanks/papers/index.html en_US
dc.subject.lcsh Cryptography en_US
dc.subject.lcsh Number theory en_US
dc.title Multiplicative Structure of Values of the Euler Function en_US
dc.type Preprint en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics


This item appears in the following Collection(s)

  • Mathematics publications (MU) [119]
    The items in this collection are the scholarly output of the faculty, staff, and students of the Department of Mathematics.

[-] show simple item record