TY - THES
AU - Kapoor, Vishaal
PY - 2011
TI - Asymptotic formulae for arithmetic functions
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/24/items/1.0080455
ER - End of Reference