Connections between Double Zeta Values relative to $μ_N$, Hecke Operators $T_N$, and Newforms of Level $Γ_0(N)$ for $N=2,3$

Ding Ma

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arXiv · 1511.06102

Connections between Double Zeta Values relative to $μ_N$, Hecke Operators $T_N$, and Newforms of Level $Γ_0(N)$ for $N=2,3$

Ding Ma

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Abstract

In this paper, we will study various connections between double zeta values relative to $μ_N$, Hecke operators $T_N$, and newforms of level $Γ_0(N)$ for $N=2,3$. Those various connections generalize the well-known of Baumard and Schneps. We also give a conjecture about the Eichler-Shimura-Manin correspondence between $\mathcal{S}_k^{\textrm{new}}(Γ_0(2))^{\pm}$, $\mathcal{S}_k^{\textrm{new}}(Γ_0(3))^{\pm}$ and some period polynomial spaces.

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Ding Ma. 2015-11-19. Connections between Double Zeta Values relative to $μ_N$, Hecke Operators $T_N$, and Newforms of Level $Γ_0(N)$ for $N=2,3$. https://arxiv.org/abs/1511.06102

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