On shuffle of double Eisenstein series in positive characteristic
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 815-825.

L’étude du présent article s’inspire du résultat de Gangl, Kaneko et Zagier sur connexion entre les valeurs zêta doubles et les formes modulaires. Nous introduisons la série d’Eisenstein double E r,s en caractéristique positive avec les valeurs zêta doubles ζ A (r,s) comme terme constant et calculons les t-expansions de la série d’Eisenstein double. De plus, on en déduit les relations de shuffle de deux séries d’Eisenstein qui correspondent aux relations de shuffle des valeurs zêta doubles dans [4].

The study of the present paper is inspired by Gangl, Kaneko and Zagier’s result of the connection with double zeta values and modular forms. We introduce double Eisenstein series E r,s in positive characteristic with double zeta values ζ A (r,s) as their constant term and compute the t-expansions of the double Eisenstein series. Moreover, we derive the shuffle relations of double Eisenstein series which match the shuffle relations of double zeta values in [4].

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DOI : https://doi.org/10.5802/jtnb.1002
Classification : 11J91,  11M36
Mots clés : Double zeta values, Eisenstein series, t-expansions, shuffle relations.
@article{JTNB_2017__29_3_815_0,
     author = {Huei-Jeng Chen},
     title = {On shuffle of double {Eisenstein} series in positive characteristic},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {815--825},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {3},
     year = {2017},
     doi = {10.5802/jtnb.1002},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1002/}
}
Huei-Jeng Chen. On shuffle of double Eisenstein series in positive characteristic. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 3, pp. 815-825. doi : 10.5802/jtnb.1002. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1002/

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