Abstract
A formula is given for the special multiple zeta values occurring in the title as rational linear combinations of products ζ(m)π2n with m odd. The existence of such a formula had been proved using motivic arguments by Francis Brown, but the explicit formula (more precisely, certain 2-adic properties of its coefficients) were needed for his proof in~\cite1 of the conjecture that all periods of mixed Tate motives over ℤ are ℚ[(2πi)±1]-linear combinations of multiple zeta values. The formula is proved indirectly, by computing the generating functions of both sides in closed form (one as the product of a sine function and a 3F2-hypergeometric function, and one as a sum of 14 products of sine functions and digamma functions) and then showing that both are entire functions of exponential growth and that they agree at sufficiently many points to force their equality. We also show that the space spanned by the multiple zeta values in question coincides with the space of double zeta values of odd weight and find a relation between this space and the space of cusp forms on the full modular group.

KEYWORDS

SHARE & LIKE

COMMENTS

SIMILAR ARTICLES

Abstract For any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a correspondin

Read MoreAbstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we

Read MoreAbstract Let L2,p(ℝ2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E⊂ℝ2 and p>2, let

Read MoreAbstract We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely

Read MoreAbstract We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We

Read MoreAbstract This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-cal

Read MoreAbstract We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for ge

Read MoreAbstract We prove that isoparametric hypersurfaces with (g,m)=(6,2) are homogeneous, which answers Dorfmeister-Neher’s conjecture affirmatively and so

Read MoreAbstract We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorificat

Read MoreAbstract If F(x,y)∈ℤ[x,y] is an irreducible binary form of degree k≥3, then a theorem of Darmon and Granville implies that the generalized superellipt

Read More