Bernhard.Heim

Affiliation: University of Cologne

Title Of Talk: Reframing the Structure and Zeros of Generalized D'Arcais Polynomials

Abstract: In this joint work with Markus Neuhauser, we investigate D'Arcais polynomials, which extend k-colored partitions and encompass all powers of the Dedekind eta function. We present new results on their zero distributions, examine their coefficients, and apply both analytic and algebraic number theoretic techniques, particularly excluding nontrivial roots of unity as zeros. We also provide a broader framework connecting combinatorial and number theoretic problems and highlight novel insights.

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