use of "restricted product" symbol (\prod and \coprod together)
- From: david.madore@xxxxxx (David Madore)
- Date: Sun, 27 Jan 2008 04:30:03 +0000 (UTC)
(Apologies if this is mildly offtopic.)
I'm looking for examples of uses of the symbol which looks like a
superimposed \prod and \coprod (or, more accurately, a product
operator whose bottom half is a mirror copy of the top half by a
horizontal axis). I'd like to suggest the addition of this character
to Unicode/ISO-10646, so the more examples I can find the more
convincing the proposal will be.
See <URL: http://www.madore.org/~david/.misc/biproduct/test.pdf > (or
test.png in the same directory) for an example (made up) formula using
this symbol. The files biproduct.{pfb,tfm} in the same directory
contain a font having the character in question.
The typical (only?) use of this symbol is in number theory to denote a
"restricted product" over places of a number field (meaning the
elements of the full product which are integral/unramified at all but
finitely many places). One example is in (at least certain editions
of) Serre's *Galois Cohomology*, in the presentation of the
Poitou-Tate sequence (page 118 of at least one edition of the book,
but I don't have it presently at hand). Unfortunately, even in this
context, it doesn't seem very common: many authors use a \prod with a
prime or something like this instead.
Thanks!
--
David A. Madore
(david.madore@xxxxxx,
http://www.madore.org/~david/ )
.
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