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Results tagged with nt.number-theory
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user 50610
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
3
votes
1
answer
289
views
Estimate sum with Euler function
(Note: this question was posted also in MSE)
I'd like to know if there's a closed formula or at least an estimate for the following (finite) sum:
$$
\sum_{D|p-1} \varphi(D) \,\varphi\left(\frac{p-1}{ …
- 215
2
votes
1
answer
275
views
sum over primes involving divisor function (variation of the Titchmarsh divisor problem)
This question was also asked on MSE.
Does there exist an asymptotic estimate for the following sum over primes
$$
\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
3
votes
1
answer
180
views
Bibliography suggestion for Kummer theory
I already posted a question about a sum involving the degree of a Kummer extension.
Now I'm interested in a more specific fact about Kummer extensions.
From Hooley's paper "On Artin's conjecture", we …
- 215