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Trinity of the Eisenstein series

Hold Date
2020-02-14 16:00〜2020-02-14 17:00
Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University
Object person
Toshiki MATSUSAKA (Kyushu university)

About a decade ago, Kaneko introduced an invariant val(w) for real quadratics as an analogue of singular moduli j(z) for imaginary quadratics. For the Faber polynomials j_n(z), it is known that the generating function of val_n(w) is close to a modular form of weight 2, and shares a similar property with the Eisenstein series E_2. Based on Rademacher’s and Ghys’ works on E_2, Duke-Imamoglu-Toth (2017) introduced the real quadratic analogue of the Rademacher symbol to study the linking numbers of modular links. In this talk, we give answers to their questions on this new object. Moreover, the limit formulas for three types of the Eisenstein series bring new perspective to them.