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Let DZk be the Q-vector space spanned by double zeta values with weight k, and DMk be its quotient space divided by the space PZk spanned by the zeta value ζ(k) and products of two zeta values with total weight k. When k is even, an upper bound for the dimension of DMk is known. By adding the dimensions of DMk and PZk, an upper bound of DZk which equals k/2 minus the dimension of the space of modular...
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