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PreprintCC BY 4.0arXiv

On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result

  • Chieh-Yu Chang
  • Song-Yun Chen
  • Fei-Jun Huang
  • Hung-Chun Tsui
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Abstract

In this paper, we study multiple Eisenstein series (MES) in positive characteristic. By computing and analyzing the t-expansions of MES, we determine the precise "weights" of their coefficients. This framework enables us to establish a graded algebra structure for MES, extending the direct sum result for Thakur's multiple zeta values proved in [Cha14]. Our result may also be viewed as a function field analogue of the corresponding direct sum result of Bachmann and Kanno [BK26].

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Cite

BibTeXRIS
BibTeX
@misc{chang2026multiple,
  title = {{On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result}},
  author = {Chieh-Yu Chang and Song-Yun Chen and Fei-Jun Huang and Hung-Chun Tsui},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18777},
  eprint = {2609.18777},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18777},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
AU  - Chieh-Yu Chang
AU  - Song-Yun Chen
AU  - Fei-Jun Huang
AU  - Hung-Chun Tsui
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.18777
UR  - https://arxiv.org/abs/2609.18777
AB  - In this paper, we study multiple Eisenstein series (MES) in positive characteristic. By computing and analyzing the t-expansions of MES, we determine the precise "weights" of their coefficients. This framework enables us to establish a graded algebra structure for MES, extending the direct sum result for Thakur's multiple zeta values proved in [Cha14]. Our result may also be viewed as a function field analogue of the corresponding direct sum result of Bachmann and Kanno [BK26].
ER  -