Zeros of even and odd period polynomials

2024/08/11 by Grace Ko, Ko, Grace, Jennifer Mackenzie +3
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2408.05670

Abstract

Let f ∈ S_k(Γ₀(N)) be a newform, and let r_f^±(X) denote its corresponding even and odd period polynomials. For sufficiently large level and weight, we show that the zeros of r_f^±(X) all lie on the circle |X| = (1)/(√ N).

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