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Multiple zeta values, multiple Eisenstein series, and period polynomials. (Japanese. English summary) Zbl 1359.11074

Summary: In this paper, we will be interested in connections between the theory of elliptic modular forms and multiple zeta values (MZVs). Recently, F. Brown [Ann. Math. (2) 175, No. 2, 949–976 (2012; Zbl 1278.19008); Adv. Stud. Pure Math. 63, 31–58 (2012; Zbl 1321.11087)] has proposed a new conjecture on the dimension of the space spanned by MZVs at the sequences indexed by odd integers greater than 1 (called totally odd MZV). His conjecture suggests that the modular forms and the linear relations among totally odd MZVs are deeply related with each other. We will give a partial answer to his conjecture in the case of depth 4 by showing that there is an injective linear map from the space of even period polynomials to the space of linear relations among totally odd MZVs. We shall also announce a result related with multiple Eisenstein series.

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11F32 Modular correspondences, etc.
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
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