Abstract
In this paper, we discuss the algebraic independence of special values of quasi-modular forms. We show that for three algebraically independent quasi-modular forms with algebraic Fourier coefficients, if one of e2πiz and their values at z in the upper half plane is a non-zero algebraic number, then the other three numbers are algebraically independent over Q. We also provide a condition for determining when quasi-modular forms are algebraically independent. Moreover, based on the theorem proved in the paper, we prove the algebraic independence of values of derivatives of modular forms with algebraic Fourier coefficients.
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