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- Asymptotic formulae for arithmetic functions
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Asymptotic formulae for arithmetic functions Kapoor, Vishaal
Abstract
In this work we will consider several questions concerning the asymptotic nature of arithmetic functions. First, we conduct a finer analysis on the behavior of λ(Euler's totient function(n)) in relation to λ(λ(n)), proving that log(λ(Euler's totient function(n))/λ(λ(n))) is asymptotic to (log log n)(log log log n)for almost all n. Second, we establish an asymptotic formula for sums of a generalized divisor function on the Gaussian numbers. And third, for complex-valued multiplicative functions that are suffciently close to 1 on the primes and bounded on prime powers, we determine the average value over a short interval x < n ≤ x+w provided the interval is suffciently long with respect to x.
Item Metadata
| Title |
Asymptotic formulae for arithmetic functions
|
| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2011
|
| Description |
In this work we will consider several questions concerning the asymptotic
nature of arithmetic functions. First, we conduct a finer analysis on the behavior
of λ(Euler's totient function(n)) in relation to λ(λ(n)), proving that log(λ(Euler's totient function(n))/λ(λ(n)))
is asymptotic to (log log n)(log log log n)for almost all n. Second, we establish
an asymptotic formula for sums of a generalized divisor function on the
Gaussian numbers. And third, for complex-valued multiplicative functions
that are suffciently close to 1 on the primes and bounded on prime powers,
we determine the average value over a short interval x < n ≤ x+w provided
the interval is suffciently long with respect to x.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-04-27
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0080455
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2011-11
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
|
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International