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The iterated Carmichael lambda function Harland, Nicholas
Abstract
The arithmetic function λ(n) is the exponent of the cyclic group (Z/nZ)^x. The k-th iterate of λ(n) is denoted by λk(n) In this work we will show the normal order for log(n/λk(n)) is (loglog n)k⁻¹}(logloglog n)/(k-1)! . Second, we establish a similar normal order for other iterate involving a combination of λ(n) and Φ(n). Lastly, define L(n) to be the smallest k such that λ_k(n)=1. We determine new upper and lower bounds for L(n) and conjecture a normal order.
Item Metadata
Title |
The iterated Carmichael lambda function
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2012
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Description |
The arithmetic function λ(n) is the exponent of the cyclic group (Z/nZ)^x. The k-th iterate of λ(n) is denoted by λk(n) In this work we will show the normal order for log(n/λk(n)) is (loglog n)k⁻¹}(logloglog n)/(k-1)! . Second, we establish a similar normal order for other iterate involving a combination of λ(n) and Φ(n). Lastly, define L(n) to be the smallest k such that λ_k(n)=1. We determine new upper and lower bounds for L(n) and conjecture a normal order.
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Genre | |
Type | |
Language |
eng
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Date Available |
2012-10-26
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution 3.0 Unported
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DOI |
10.14288/1.0073354
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2013-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution 3.0 Unported