On the Atkin $U_t$-operator for $\Gamma_1(t)$-invariant Drinfeld cusp forms

Andrea Bandini; Maria Valentino

On the Atkin $U_t$-operator for $\Gamma_1(t)$-invariant Drinfeld cusp forms

Number Theory 2017-10-04 v1

Authors: Andrea Bandini , Maria Valentino

Abstract

We study the diagonalizability of the Atkin $U_t$ -operator acting on Drinfeld cusp forms for $\Gamma_1(t)$ and $\Gamma(t)$ 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.

Keywords

Atkin U_t-operator Drinfeld cusp forms diagonalizability harmonic cocycles Gamma_1(t)-invariant modular forms characteristic

Cite

@article{arxiv.1710.01036,
  title  = {On the Atkin $U_t$-operator for $\Gamma_1(t)$-invariant Drinfeld cusp forms},
  author = {Andrea Bandini and Maria Valentino},
  journal= {arXiv preprint arXiv:1710.01036},
  year   = {2017}
}

Comments

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

On the Atkin $U_t$-operator for $\Gamma_1(t)$-invariant Drinfeld cusp forms

Abstract

Keywords

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