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Old 2019-08-06, 01:32   #1
Andrew99
 
Aug 2019

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Default Help : Deriving an inequality

Hi, I am studying a paper by Yann Bugeaud (click here), on page 13 there is an inequality (16) as given below image-

https://www.mersenneforum.org/attach...1&d=1565055006

which is obtained from the below image file -

https://www.mersenneforum.org/attach...1&d=1565055006

, on page 12.

How the inequality (16) is derived? I couldn't figure it out. However one of my forum member tried but it has two problems (problems are marked as "how?"), it is given in below image-

https://www.mersenneforum.org/attach...1&d=1565055006

It is not clear how those two questions would be resolved.

Can any one show the derivation of inequality (16)?




Thanks in Advance.
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Old 2019-08-06, 03:07   #2
Uncwilly
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So, you didn't find help over here:
https://www.freemathhelp.com/forum/t...quence.117311/

Since the post is identical except the image attachments it looks like you copied and pasted. Can you give us some more background?
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Old 2019-08-06, 04:51   #3
Andrew99
 
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No I did not get any help from there, you can find all detail in page 12 an 13 of the paper, not much detail is given.
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Old 2019-08-06, 22:51   #4
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The symbol \ll isn't just an inequality symbol. In analytic number theory, if f and g are functions of one variable (in particular, a positive integer variable)

f(x)\;\ll\;g(x)

indicates that there is a (positive) constant k such that

f(n) \;\le\; k\cdot g(n)

for sufficiently large n. The notation is due to Vinogradov.
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