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Old 2009-12-24, 20:59   #1
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Default 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).
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Old 2009-12-25, 03:18   #2
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To be more precise, what is the best lower-bound on \Psi(x,y)?

Anyone? It's awfully quite on this thread
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Old 2009-12-25, 03:24   #3
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Quote:
Originally Posted by flouran View Post
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.
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Old 2009-12-25, 03:25   #4
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Quote:
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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?
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Old 2009-12-25, 03:32   #5
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Quote:
Originally Posted by flouran View Post
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?
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Old 2009-12-25, 03:33   #6
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Quote:
Originally Posted by retina View Post
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.
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Old 2009-12-25, 05:32   #7
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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
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Old 2009-12-25, 08:50   #8
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Quote:
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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
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Old 2009-12-25, 09:26   #9
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Quote:
Originally Posted by xilman View Post
Why, what's happening?
I think it is flouran avoidance day. But don't tell him.
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Old 2009-12-25, 11:24   #10
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Quote:
Originally Posted by retina View Post
I think it is flouran avoidance day. But don't tell him.
http://www.youtube.com/watch?v=TXdk4DOPgM8

Last fiddled with by davieddy on 2009-12-25 at 11:28 Reason: Found an infinitely better version:)
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Old 2009-12-25, 13:28   #11
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Quote:
Originally Posted by retina View Post
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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