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math.NT2026
An Algebraic Proof of the Non-Modularity of Solutions to the Canonical Modular Differential Equation
Yuichi Sakai, Hiroyuki Tsutsumi
In this paper, we provide an algebraic proof of the condition for the existence of modular form solutions to the Kaneko-Zagier differential equation of weight . Unlike previous…
math.NT2026
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…