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 2009-12-24, 20:59 #1 flouran     Dec 2008 72·17 Posts Distribution of Smooth Numbers Is anyone aware of either Hildebrand's or Tenenbaum's work on the distribution of smooth numbers? I have heard of their precise approximations for this distribution and thus was wondering if they were either in the form of papers and/or books? If the former, then please let me know of the title of the paper(s) (and if possible you can send me the electronic version of the paper(s) via email), and if the latter then please inform me of the title(s).
 2009-12-25, 03:18 #2 flouran     Dec 2008 72×17 Posts To be more precise, what is the best lower-bound on $\Psi(x,y)$? Anyone? It's awfully quite on this thread
2009-12-25, 03:24   #3
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

41×149 Posts

Quote:
 Originally Posted by flouran Anyone? It's awfully quite on this thread
Considering the date I think you should give a little more time before declaring that everyone has abandoned you.

2009-12-25, 03:25   #4
flouran

Dec 2008

72×17 Posts

Quote:
 Originally Posted by retina Considering the date I think you should give a little more time before declaring that everyone has abandoned you.
Any ideas then on the lower-bound?

2009-12-25, 03:32   #5
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

41·149 Posts

Quote:
 Originally Posted by flouran Any ideas then on the lower-bound?
Is it 1? Or is it a trick question? For most mathematical problems I usually just use brute force, and if I haven't got the answer before reaching 10 I just give up. Perhaps this method will work for you also?

2009-12-25, 03:33   #6
flouran

Dec 2008

72·17 Posts

Quote:
 Originally Posted by retina Is it 1? Or is it a trick question? For most mathematical problems I usually just use brute force, and if I haven't got the answer before reaching 10 I just give up. Perhaps this method will work for you also?
Not at all a trick question. Hopefully others will be able to contribute. If I find the answer myself, I shall post here.

 2009-12-25, 05:32 #7 Robert Holmes     Oct 2007 11010102 Posts Not being an expert on the topic, this looks like a good place to start (if not just to harvest references): "Smooth numbers: computational number theory and beyond" http://www.math.leidenuniv.nl/~psh/ANTproc/09andrew.pdf Last fiddled with by Robert Holmes on 2009-12-25 at 05:37
2009-12-25, 08:50   #8
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

73·31 Posts

Quote:
 Originally Posted by retina Considering the date I think you should give a little more time before declaring that everyone has abandoned you.
Why, what's happening?

I thought it was rather quiet, both on the forum and on the roads. No rush-hour traffic, even though most of the snow has now cleared from around here.

Very strange.

Paul

Last fiddled with by xilman on 2009-12-25 at 08:50 Reason: Fix tyop

2009-12-25, 09:26   #9
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

17DD16 Posts

Quote:
 Originally Posted by xilman Why, what's happening?
I think it is flouran avoidance day. But don't tell him.

2009-12-25, 11:24   #10
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by retina I think it is flouran avoidance day. But don't tell him.

Last fiddled with by davieddy on 2009-12-25 at 11:28 Reason: Found an infinitely better version:)

2009-12-25, 13:28   #11
davieddy

"Lucan"
Dec 2006
England

194A16 Posts

Quote:
 Originally Posted by retina I think it is flouran avoidance day. But don't tell him.
I've just thought or a great title for my new book:

"How to win friends and influence people"

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