Re: Transcendental Dimensions

=?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= <jcsantos@xxxxxxxx> writes:

>On 21-07-2005 11:48, Lee Rudolph wrote:
>
>>>Not exactly, the author merely says that *a* proof can be found in the
>>>cited 1979 publication by Hardy & Wright.
>>
>>
>> There were no 1979 publications by Hardy & Wright.
>
>1979 is the year in which the fifth edition of their book was published.

....which was in no reasonable sense a publication "by Hardy & Wright"
(in the usual sense of "&"). Here is part of Apostol's Mathematical
Reviews note on that edition.

===begin===
After Hardy's death in 1947, Professor Wright refrained from more
thorough revisions for fear of disturbing Hardy's unique style.
The most important changes in subsequent editions were the addition
of an elementary proof of the prime number theorem in the third
(1954) edition and an index of names in the fourth (1960) edition.
Each new edition has also seen minor changes such as simplification
of some proofs and updating of the Notes. A new Theorem 272 in the
fourth edition evaluates Ramanujan's sum in terms of the Moebius
function and the Euler totient.

The main changes in this latest edition are in the Notes and in the
index of names. A short two-page appendix at the end of the book
mentions some recent advances concerning prime numbers, such as the
work of Davis, Matijasevi\v c, Putnam and Robinson on constructing
a polynomial $R(x_1,\cdots,x_k)$ whose positive values are primes
for nonnegative integer values of $x_1,\cdots,x_k$, and recent
progress toward the solution of Goldbach's conjecture. An interesting
observation is that none of the unsolved problems on primes mentioned
in the first edition has been completely settled in the intervening
40 years.
===end===

I see no mention of the Gelfond-Schneider theorem (or its special
case previously mentioned) there, and deduce that the correct
scholarly citation for the Hardy & Wright proof of the G-S theorem
(or its special case) would have been to the first, 1938, edition.

Sheesh. If a person can't be a pedant in sci.math, where *can*
a person be a pedant?

Lee Rudolph
.

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