Abstract:We prove that the field generated by the Fourier coefficients of weakly holomorphic Poincaré series of a given level $$\varGamma _0(N)$$
Γ
0
(
N
)
and integral weight $$k\ge 2$$
k
≥
2
coincides with the field generated by the single-valued periods of a certain motive attached to $$\varGamma _0(N)$$
Γ
0
(
N
)
. This clarifies the arithmetic nature of such Fourier coefficients and generalises previous formulas of Brown and Acres–Broadhurst giving explicit series expansions for the single-valued p… Show more
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