Polynomial Identities on Eigenforms
classification
🧮 math.NT
keywords
polynomialeigenformsfixedidentitiescasescoefficientscomplexdetermine
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In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases, only finitely many such identities hold for a fixed polynomial.
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