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arXiv · 2410.20385

Rationality of the periods of Eisenstein series

Soumyadip Sahu
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Abstract

The article generalizes an observation of Zagier and Gangl to show that the image of the spectral Eisenstein series on a general congruence subgroup of $\text{SL}_2(\mathbb{Z})$, under the Eichler-Shimura isomorphism, is defined over a cyclotomic number field. We use the same technique to generalize an invariant attached to imaginary quadratic fields in connection with the polylogarithm conjecture on the special values of $L$-functions. Our treatment also provides an elementary derivation of the Fourier expansion of the Maass Eisenstein series on congruence subgroups presented as a power series.

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Soumyadip Sahu. 2024-10-27. Rationality of the periods of Eisenstein series. https://arxiv.org/abs/2410.20385

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