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Results tagged with asymptotics
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user 50610
Asymptotic behavior of functions, asymptotic series and related topics
2
votes
1
answer
275
views
sum over primes involving divisor function (variation of the Titchmarsh divisor problem)
This question was also asked on MSE.
Does there exist an asymptotic estimate for the following sum over primes
$$
\sum_{p\leq x} \frac{\tau(p-1)}{p}\;,
$$
where $\tau(n)=\sum_{d|n}1$ is the divisor fu …
- 215
3
votes
1
answer
177
views
Doubt concerning a sum involving Kummer extension degrees
I'd like to estimate the following sum
$$
\sum_{n\leq x}\frac1{k_n}\;,\qquad x\rightarrow \infty\;,
$$
where
$k_n=[\mathbb{Q}(\zeta_n,a^{1/n}):\mathbb{Q}]$
is the degree of a Kummer extension for a f …
- 215