Combinatorial multiple Eisenstein series

Bachmann H, Burmester A (2023)
Research in the Mathematical Sciences 10(3): 35.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bachmann, Henrik; Burmester, AnnikaUniBi
Abstract / Bemerkung
We construct a family of q-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given Q-valued solution of the extended double shuffle equations. We call these q-series combinatorial (bi-)multiple Eisenstein series, and in depth one they coincide with (classical) Eisenstein series. Combinatorial multiple Eisenstein series can be seen as an interpolation between the given Q-valued solution of the extended double shuffle equations (as q ? 0) and multiple zeta values (as q ? 1). In particular, they are q-analogues of multiple zeta values closely related to modular forms. Their definition is inspired by the Fourier expansion of multiple Eisenstein series introduced by Gangl-Kaneko-Zagier. Our explicit construction is done on the level of their generating series, which we show to be a so-called symmetril and swap invariant bimould.
Stichworte
Multiple zeta values; Double shuffle equations; Eisenstein series; Modular forms
Erscheinungsjahr
2023
Zeitschriftentitel
Research in the Mathematical Sciences
Band
10
Ausgabe
3
Art.-Nr.
35
ISSN
2522-0144
eISSN
2197-9847
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2981955

Zitieren

Bachmann H, Burmester A. Combinatorial multiple Eisenstein series. Research in the Mathematical Sciences. 2023;10(3): 35.
Bachmann, H., & Burmester, A. (2023). Combinatorial multiple Eisenstein series. Research in the Mathematical Sciences, 10(3), 35. https://doi.org/10.1007/s40687-023-00398-8
Bachmann, Henrik, and Burmester, Annika. 2023. “Combinatorial multiple Eisenstein series”. Research in the Mathematical Sciences 10 (3): 35.
Bachmann, H., and Burmester, A. (2023). Combinatorial multiple Eisenstein series. Research in the Mathematical Sciences 10:35.
Bachmann, H., & Burmester, A., 2023. Combinatorial multiple Eisenstein series. Research in the Mathematical Sciences, 10(3): 35.
H. Bachmann and A. Burmester, “Combinatorial multiple Eisenstein series”, Research in the Mathematical Sciences, vol. 10, 2023, : 35.
Bachmann, H., Burmester, A.: Combinatorial multiple Eisenstein series. Research in the Mathematical Sciences. 10, : 35 (2023).
Bachmann, Henrik, and Burmester, Annika. “Combinatorial multiple Eisenstein series”. Research in the Mathematical Sciences 10.3 (2023): 35.
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2024-07-01T14:02:56Z
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