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On modular forms of rational weight satisfying the canonical second-order linear modular differential equation
Yuichi Sakai, Hiroyuki Tsutsumi
In this paper, we completely classify the rational weights for which the Kaneko-Zagier (KZ) differential equation admits a fundamental system of solutions consisting of modular…
Minimal models, modular linear differential equations and modular forms of fractional weights
Kiyokazu Nagatomo, Yuichi Sakai
We show that modular forms of fractional weights on principal congruence subgroups of odd levels, which are found by T. Ibukiyama, naturally appear as characters being multiplied $…
Modular Linear Differential Operators and Generalized Rankin-Cohen Brackets
Kiyokazu Nagatomo, Yuichi Sakai, Don Zagier
The aim in this paper is to give expressions for modular linear differential operators of any order. In particular, we show that they can all be described in terms of Rankin-Cohen…
Modular parametrizations of certain elliptic curves
Matija Kazalicki, Yuichi Sakai, Koji Tasaka
Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a parti…