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 Post subject: Asymptotic (Number Theory)Posted: Thu, 5 Nov 2009 17:44:00 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
My friend Eric told me this one, and I thought it interesting enough to post.

Consider the formula

(p ranges over the primes)

Find a function of an analytic variable, , such that

.

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 Post subject: Re: Asymptotic (Number Theory)Posted: Wed, 11 Nov 2009 15:00:16 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7624
Location: NCTS/TPE, Taiwan
Shadow wrote:
My friend Eric told me this one, and I thought it interesting enough to post.

Consider the formula

(p ranges over the primes)

Find a function of an analytic variable, , such that

.

Presumably you can take a branch cut?

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 Post subject: Re: Asymptotic (Number Theory)Posted: Thu, 12 Nov 2009 02:28:26 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15563
Location: Austin, TX
outermeasure wrote:
Shadow wrote:
My friend Eric told me this one, and I thought it interesting enough to post.

Consider the formula

(p ranges over the primes)

Find a function of an analytic variable, , such that

.

Presumably you can take a branch cut?

Yes. And the right one is fairly obvious I would say.

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