2024/10/27 by Soumyadip Sahu, Sahu, Soumyadip
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2410.20385
openalex publication_date 2024/10/27 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
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 SL2(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.