Work

Equations involving the modular 𝑗-function and its derivatives

Year: 2025

Type: article

Abstract: We show that, for any polynomial F ⁢ ( X , Y 0 , Y 1 , Y 2 ) ∈ C ⁢ [ X , Y 0 , Y 1 , Y 2 ] F(X,Y_{0},Y_{1},Y_{2})\in\mathbb{C}[X,Y_{0},Y_{1},Y_{2}] , the equation F ⁢ ( z , j ⁢ ( z ) , j ′ ⁢ ( z ) , j ′′ ⁢ ( z ) ) = 0 F(z,j(z),j^{\prime}(z),j^{\prime\prime}(z))=0 has a Zariski dense set of solutions in the hypersurface F ⁢ ( X , Y 0 , Y 1 , Y 2 ) = 0 F(X,Y_{0},Y_{1},Y_{2})=0 , unless 𝐹 is in C ⁢ [ X ] \mathbb{C}[X] or it is divisible by Y 0 Y_{0} , Y

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0067

Authors: Vahagn Aslanyan, Sebastian Eterović, Vincenzo Mantova

Institutions: University of Manchester, University of Vienna, University of Leeds

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: Leverhulme Trust, Engineering and Physical Sciences Research Council