From wstein@ucsd.edu Thu Feb 16 19:22:11 2006
From: William Stein <wstein@ucsd.edu>
Organization: UC San Diego
To: Barry Smith <barryrsmith@gmail.com>
Subject: Re: bernfrac
Date: Thu, 16 Feb 2006 19:22:11 -0800
User-Agent: KMail/1.9.1
References: <200601082158.34196.wstein@ucsd.edu> <200602161704.01083.wstein@ucsd.edu> <5850a51c0602161919x6d1afc56uf5a7d23134a01225@mail.gmail.com>
In-Reply-To: <5850a51c0602161919x6d1afc56uf5a7d23134a01225@mail.gmail.com>
X-KMail-Link-Message: 558034
X-KMail-Link-Type: reply
MIME-Version: 1.0
Content-Type: text/plain;
  charset="utf-8"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
Message-Id: <200602161922.11824.wstein@ucsd.edu>
Status: RO
X-Status: RSC
X-KMail-EncryptionState:  
X-KMail-SignatureState:  
X-KMail-MDN-Sent:  

On Thursday 16 February 2006 19:19, you wrote:
> these two forms, only two Bernoulli numbers need to be calculated mod p to
> determine the class number, so most of the Bernoulli numbers are not
> needed.  Perhaps Joe Buhler's algorithm could do this quickly. 

You're right -- Joe's algorithm computes all Bernoulli numbers up to 10^7 
(say) modulo a single prime p. 

> of fields of higher degree than 3.  This is a good excuse to commence work
> on that project.

Sounds good. 

> By the way, I was wondering on the way home how efficient it would be to
> calculate B_{n} by interpolating the sums of the nth powers of the first k
> natural numbers for k=1 to n+1 with an n+1 degree polynomial and read of
> the constant coefficient.  I suppose these sums might involve too many
> computations.

That sounds to me like a really really hard way to do it compared to the 
existing methods... but I could be wrong.

william