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Huei-Jeng Chen
On shuffle of double Eisenstein series in positive characteristic
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 815-825, doi: 10.5802/jtnb.1002
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Class. Math.: 11J91, 11M36
Keywords: Double zeta values, Eisenstein series, $t$-expansions, shuffle relations.

Résumé - Abstract

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 $\zeta _A(r,s)$ 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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