Rationality of the periods of Eisenstein series
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908513335246848 |
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| author | Sahu, Soumyadip |
| author_facet | Sahu, Soumyadip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20385 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rationality of the periods of Eisenstein series Sahu, Soumyadip Number Theory 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. |
| title | Rationality of the periods of Eisenstein series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.20385 |