Multiple Eisenstein Series

Research Meeting

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Recently, multiple Eisenstein series of arbitrary rank r ≥ 1 in positive characteristic were introduced and studied. In this talk, we will discuss an analogue of the Goncharov–Zagier direct sum conjecture in this setting. Our result may also be viewed as a function field counterpart of the recent direct sum theorem of Bachmann and Kanno. This talk is based on joint work with C.-Y. Chang, S.-Y. Chen, and F.-J. Huang.

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In this talk, we discuss the distribution of zeros of the multiple Eisenstein series G_{2}ⁿ, which is a quasimodular form. In particular, we present a method for studying the number of zeros without using the Rankin–Swinnerton-Dyer method, which has played an important role in previous studies of the zeros of Eisenstein series. This talk is based on joint work with Gyucheol Shin of Kangwon National University.