From: Fred W. Helenius Subject: Re: ?: Newmans Proof of the Prime Number Theorem Date: Fri, 14 Apr 2000 19:03:49 -0400 Newsgroups: sci.math Summary: [missing] Florian Wessels wrote: >There is a book (Geometric and analytic Number Theory, Hlawka et al, >Springer Universitext), in which there is a short proof of the PNT >which was given by Newman (1980). Well, so the authors say... >Does anyone know where (and when) which Newman published this proof? The original article is D. J. Newman, Simple analytic proof of the prime number theorem, American Mathematical Monthly, vol. 87 #9, 1980, 693-696. Two further expositions of Newman's proof are J. Korevaar, On Newman's quick way to the prime number theorem, Mathematical Intelligencer, vol. 4 #3, 1982, 108-115, and D. Zagier, Newman's Short Proof of the Prime Number Theorem, American Mathematical Monthly, October 1997, 705-709. Zagier was awarded the Chauvenet Prize for mathematical exposition for his article. -- Fred W. Helenius ============================================================================== From: Don Redmond Subject: Re: Prime number theorem: proof? Date: Fri, 14 Apr 2000 21:29:01 -0500 Newsgroups: sci.math In article , Jan Kristian Haugland wrote: > On Thu, 13 Apr 2000 prova9975@my-deja.com wrote: > > > Prime number theorem: proof? > > > > Hello > > > > Where can I find (on the web?) a proof of the "Prime Number Theorem"? > > (The number of primes not exceeding x is asymptotic to x/log x ) > > It can be found in "Multiplicative Number Theory" by Davenport. > If you don't like complex variables you can try Hardy and Wright, Intro to Number Theory. They give a version of a real variable proof. Also someone, whose name escapes me at the moment, published a paper in Amer. Math. Monthly in the 1960s sometime called A Motivated Account of the Prime Number Theorem. It too is a real varables proof. Finally, if you don't mind complex variables and want to see a proof that proves directly pi(x) ~ x/log(x), see Grosswald, Topics in the Theory of Numbers. Hope that helps. Don ============================================================================== From: bumby@lagrange.rutgers.edu (Richard Bumby) Subject: Re: DJN's Short Route to the Prime # thm Date: 8 May 2000 16:43:43 -0400 Newsgroups: sci.math panok@erols.com (pnk) writes: >I beleive it was first published in the american mathematical monthly. >I don't remember the month but I (nearly) certain the year was 1980. >I think he gave two profs in that article. >He also wrote a book w/Joseph BAK called "Complex Analysis", it's a >springer UTM book. The proof appears there as well. >hope this helps The year was a big clue. It is the lead article in the November, 1980 issue (page 693 for those working with bound issues). Subsequent articles in the Monthly related to this appeared in November, 1996 (by Bateman and Diamond), and October, 1997 (by Zagier).