Timeline for Lower bound of the number of relatively primes(each-other) in an interval
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 25, 2011 at 19:45 | history | edited | Gerhard Paseman | CC BY-SA 2.5 |
added 324 characters in body
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| Feb 24, 2011 at 17:41 | comment | added | Asterios Gkantzounis | Thank you, I will send an e-mail to Will Jagy,regards | |
| Feb 23, 2011 at 21:17 | history | edited | Gerhard Paseman | CC BY-SA 2.5 |
one more tweak
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| Feb 23, 2011 at 21:08 | comment | added | Gerhard Paseman | I got my n's confused. Yes, for any positive real number K there is n_0 such that for all n > n_0 there is an interval of length Kn in which every integer has a factor among the first n primes. Thanks for doing the thinking for me. I withdraw my pi(other n/2) lower bound claim. Send Will Jagy an email mentioning this comment; he will forward it to me. Alternatively, point me toward your email. I can send you a few pages of the article by email after I have scanned them. If you can finish those, then I will send you more. Gerhard "Ask Me About System Design" Paseman, 2011.02.23 | |
| Feb 23, 2011 at 17:58 | comment | added | Asterios Gkantzounis | do you want my email in order to send me the original article in german? | |
| Feb 23, 2011 at 17:57 | comment | added | Asterios Gkantzounis | the theory implies that for any K natural there is an n such that there is an interval of length Kn that every number in it is divisible by the first pi(n) numbers so in this there are at most pi(n) coprimes so you cant have alower bound of this form .Not? | |
| Feb 23, 2011 at 17:08 | comment | added | Gerhard Paseman | Maybe there is an implication, but I don't see it now. Using the notation of the "cool upper bound argument" question, Westzynthius also provides an asymptotic lower bound for max (q_{i+1} - q_i) of the form p_n log(p_n) h(p_n) where h involves iterated logs and 1/h is dominated by log . You might be able to use it for Gerry Myerson's reformulation. Although I have no proof yet, I am confident of pi(n/2) as a lower bound. Gerhard "Ask Me About System Design" Paseman, 2011.02.23 | |
| Feb 23, 2011 at 16:48 | comment | added | Asterios Gkantzounis | the theorem of westzynthious does not implie that there is not a lower bound of the form $π(an)$ where a is a positive rational? | |
| Feb 21, 2011 at 7:37 | comment | added | Gerhard Paseman | No (as far as I know), but I may be able to send you a copy of the original German article. (Especially if you can send me a copy of D. & P.'s oscillation article!) Also, after I finish my writeup to my question on this, I can provide a summary in English of much of W.'s article. Gerhard "Ask Me About System Design" Paseman, 2011.02.20 | |
| Feb 21, 2011 at 7:18 | comment | added | Asterios Gkantzounis | @Gerhard:Is the Weszynthious article anywhere free on the internet? Thank you for the answer | |
| Feb 20, 2011 at 22:29 | history | edited | Gerhard Paseman | CC BY-SA 2.5 |
fixed typo
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| Feb 20, 2011 at 22:21 | comment | added | Gerhard Paseman | PPS, I have access to Carella's refinement of Diamond and Pintz, but won't spend as much time on it unless I get trusted assurances that it is worth spending much time reviewing. Gerhard "Won't Review Much For Free" Paseman, 2011.02.20 | |
| Feb 20, 2011 at 22:18 | comment | added | Gerhard Paseman | Not being a subscriber to Journal de Théorie des Nombres de Bordeaux, I would be grateful to (willing to barter with) anyone who gave me (an English version preferably of) vol. 21 (2009), 523-533 Oscillation of Mertens' product formula, or a nice function h(n) and assurances (proof) that 1/h(n)ln(n ln(n)) is less than the nth Mertens product. Gerhard "Will Estimate For Money/Preprints" Paseman, 2011.02.20 | |
| Feb 20, 2011 at 22:06 | history | edited | Gerhard Paseman | CC BY-SA 2.5 |
fixed tex part 2
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| Feb 20, 2011 at 22:01 | history | answered | Gerhard Paseman | CC BY-SA 2.5 |