Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that the multiple zeta sum: ζ(s 1 , s 2 ,...,s d ) = Σ  n1>n2>...>nd  1/n s1  1 n s2  2 ...n sd  d  for positive integers s i  with S 1  > 1, 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 d one may resolve D good digits of ζ in O(D log D/ log log D) arithmetic operations, with the implied big-O constant depending only on the set {s 1 ,..., s d }.
['Richard E. Crandall']
I am writing a research paper on a idea Fast evaluation of multiple zeta sums
[{"from": "human", "value": "I am writing a research paper on a idea Fast evaluation of multiple zeta sums"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that the multiple zeta sum: \u03b6(s 1 , s 2 ,...,s d ) = \u03a3  n1>n2>...>nd  1/n s1  1 n s2  2 ...n sd  d  for positive integers s i  with S 1  > 1, 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 d one may resolve D good digits of \u03b6 in O(D log D/ log log D) arithmetic operations, with the implied big-O constant depending only on the set {s 1 ,..., s d }."}]