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answered How would you show $\pi(x)\log(1-\frac{1}{x}) \sim \frac{1}{\log x}$
Aug
15
accepted Finding the transfinite diameter of the level sets of complex logarithm
Aug
15
comment Finding the transfinite diameter of the level sets of complex logarithm
@900sit-upsaday: Maybe you can expand this into an answer?
Aug
15
comment Why are people more interested in the Riemann hypothesis than Goldbach's conjecture?
This should be CW (and I think it should stay open).
Aug
14
answered Fastest way to find if a given number is prime
Aug
14
comment Finding the transfinite diameter of the level sets of complex logarithm
@900sit-upsaday: I added my personal translation (all I have) of the relevant excerpt.
Aug
14
revised Finding the transfinite diameter of the level sets of complex logarithm
add translation from paper
Aug
13
comment Finding the transfinite diameter of the level sets of complex logarithm
@HagenvonEitzen: I don't think so. The point is to find the transfinite diameter for a given $C$ and adjust the value of $C$ until the transfinite diameter is at a desired value, and the distance between the bounding disks that I'd only get ~1 decimal place of accuracy if I did that.
Aug
13
revised Finding the transfinite diameter of the level sets of complex logarithm
restrict problem statement
Aug
13
comment Iterated Pi function
@vukov: Agreed. That's another manifestation of $n$ growing with $x$.
Aug
13
comment Strongest 'average' for a diverse set of numbers?
You may wish to clarify what you mean by "strongest", as the two current answers assume different interpretations.
Aug
13
answered Strongest 'average' for a diverse set of numbers?
Aug
13
comment Iterated Pi function
@JackM: Also A007097, where a(n) is the least number such that $\pi_n(a(n))=1.$
Aug
13
answered Iterated Pi function
Aug
13
awarded  Nice Answer
Aug
12
comment Finding the transfinite diameter of the level sets of complex logarithm
@zibadawatimmy: The author, Pisot, died 30 years ago. The paper is Sur les fonctions arithmétiques analytiques à croissance exponentielle, C. R. Acad. Sc. Paris 222 and the result is on p. 988.
Aug
12
comment Finding the transfinite diameter of the level sets of complex logarithm
@zibadawatimmy: My particular example comes from a research paper I read which gives no explanation of the map, just a calculation of what the transfinite diameter comes to with certain $C$. Because it omitted all details I supposed that this was considered routine. Is there a way to do it?
Aug
12
comment Gradient descent vs. Newton's method — which one requires more computation?
@user72694: If you have to compute the derivative at each step (at the same cost as computing the function) then Newton's method is suboptimal and the secant method does better. If you get the derivative calculation for free -- perhaps as a side-effect of computing the function -- then Newton is faster than secant.
Aug
12
revised Finding the transfinite diameter of the level sets of complex logarithm
simplify
Aug
12
answered Decide to use Factorials or nCr