On the Atkin U_t-operator for Γ₁(t)-invariant Drinfeld cusp forms

2017/10/03 by Andrea Bandini, Bandini, Andrea, Maria Lucia Valentino +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1710.01036

It contains parts of the previous arXiv:1702.08801 [math:NT], which has now been split in two papers with some new results

arxiv created 2017/10/03 · openalex publication_date 2017/10/03 · arxiv updated 2017/10/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study the diagonalizability of the Atkin U_t-operator acting on Drinfeld cusp forms for Γ₁(t) and Γ(t) using Teitelbaum's interpretation as harmonic cocycles. For small weights k\leqslant 2q, we prove U_t is diagonalizable in odd characteristic and we point out that non diagonalizability in even characteristic depends on antidiagonal blocks.

Citations

• On the diagonalizability of the Atkin U-operator for Drinfeld cusp forms

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• On the diagonalizability of the Atkin U-operator for Drinfeld cusp forms

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