Atlas home ||
Conferences |
Abstracts |
about Atlas
Turku Symposium on Number Theory in Memory of Kustaa Inkeri
May 31 - June 4, 1999
University of Turku
Turku, Finland |
|
Organizers
Matti Jutila, Tauno Metsänkylä
View Abstracts
Conference Homepage |
Multiple Zeta Sums Via Box Splines
by
Karl Dilcher
Dalhousie University, Halifax, Nova Scotia, Canada
Coauthors: Kirk Haller
In the ``language" of box splines, the Poisson summation formula is used to
evaluate multiple series of the type
|
|
å
j in Zs
|
|
1
(a11j1+ ... +as1js-x1)2m1 ... (a1nj1+ ... +asnjs-xn)2mn
|
, |
|
where aij in Z and m1, ... , mn in N.
The case s=n is studied in greater detail, and a criterion for the
factoring of the multiple series into a product of simple series is given.
The case x1= ... = xn=0 is also studied in detail. In all cases the sum
of the multiple series is the product of an algebraic number and
\pi2(m1+ ... +mn). This can be seen as a generalization of Euler's
formula for the Riemann zeta function at even positive integers.
Date received: March 29, 1999
Copyright © 1999 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cacf-16.