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- W1998307257 abstract "For positive integers α1,α2,…,αr with αr⩾2, the multiple zeta value or r-fold Euler sum is defined asζ(α):=ζ(α1,α2,…,αr)=∑1⩽k1<k2<⋯<krk1−α1k2−α2⋯kr−αr. There is a celebrated sum formula among multiple zeta values as∑|α|=mζ(α1,α2,…,αr+1)=ζ(m+1), where α1,α2,…,αr range over all positive integers with |α|=α1+α2+⋯+αr=m in the summation. In this paper, we shall prove that for all positive integers m and q with m⩾q, and a nonnegative integer p,∑|α|=mζ({1}p,α1,α2,…,αq+1)=∑|c|=p+qζ(c1,c2,…,cp+1+(m−q)+1). When p=0 and q=r, this is precisely the sum formula. Such a formula can be used to determine explicitly, some multiple zeta values of lower weights more precisely than the sum formula." @default.
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- W1998307257 date "2009-04-01" @default.
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- W1998307257 title "A restricted sum formula among multiple zeta values" @default.
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- W1998307257 doi "https://doi.org/10.1016/j.jnt.2008.07.012" @default.
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