Abstract
Let A be a polynomial ring in one variable over a finite field and k be its fraction field. Let f be a Drinfeld modular form of nonzero weight for a congruence subgroup of GL2(A) so that the coefficients of the q ∞-expansion of f are algebraic over k. We consider n CM points α 1, . . . , α n on the Drinfeld upper half plane for which the quadratic fields k(α 1), . . . , k(α n ) are pairwise distinct. Suppose that f is non-vanishing at these n points. Then we prove that f(α 1), . . . , f(α n ) are algebraically independent over k.
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C.-Y. Chang was supported by an NCTS postdoctoral fellowship.
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Chang, CY. Special values of Drinfeld modular forms and algebraic independence. Math. Ann. 352, 189–204 (2012). https://doi.org/10.1007/s00208-011-0633-8
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DOI: https://doi.org/10.1007/s00208-011-0633-8