On the trace and norm maps from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$

Christelle Vincent

On the trace and norm maps from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$

Number Theory 2014-06-17 v1

Authors: Christelle Vincent

Abstract

Let $f$ be a Drinfeld modular form for $\Gamma_0(\mathfrak{p})$ . From such a form, one can obtain two forms for the full modular group $\operatorname{GL}_2(A)$ : by taking the trace or the norm from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$ . In this paper we show some connections between the arithmetic modulo $\mathfrak{p}$ of the coefficients of the $u$ -series expansion of $f$ and those of a form closely related to its trace, and of the coefficients of $f$ and those of its norm.

Keywords

Drinfeld modular forms trace map norm map congruence subgroups arithmetic modulo p u-series expansion GL2(A)

Cite

@article{arxiv.1406.3879,
  title  = {On the trace and norm maps from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$},
  author = {Christelle Vincent},
  journal= {arXiv preprint arXiv:1406.3879},
  year   = {2014}
}

On the trace and norm maps from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$

Abstract

Keywords

Cite

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