Fast evaluation of multiple zeta sums

Author:
Richard E. Crandall

Journal:
Math. Comp. **67** (1998), 1163-1172

MSC (1991):
Primary 11Y60, 11Y65; Secondary 11M99

MathSciNet review:
1459385

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the multiple zeta sum:

for positive integers with , can always be written as a finite sum of products of rapidly convergent series. Perhaps surprisingly, one may develop fast summation algorithms of such efficiency that the overall complexity can be brought down essentially to that of *one*-dimensional summation. In particular, for any dimension one may resolve good digits of in arithmetic operations, with the implied big- constant depending only on the set .

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Additional Information

**Richard E. Crandall**

Affiliation:
Center for Advanced Computation, Reed College, Portland, Oregon 97202

Email:
crandall@reed.edu

DOI:
http://dx.doi.org/10.1090/S0025-5718-98-00950-8

Received by editor(s):
September 30, 1996

Received by editor(s) in revised form:
March 3, 1997

Article copyright:
© Copyright 1998
American Mathematical Society