A product formula for the higher rank Drinfeld discriminant function

Dirk Basson

doi:10.1016/j.jnt.2017.02.010

A product formula for the higher rank Drinfeld discriminant function

Number Theory 2023-02-14 v1

Authors: Dirk Basson

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Abstract

We give a product expansion for the Drinfeld discriminant function in arbitrary rank $r$ , which generalizes the formula obtained by Gekeler for the rank 2 Drinfeld discriminant function. This enables one to compute the Fourier expansion of this function much more efficiently. The formula in this article uses an $r-1$ -dimensional parameter and as such provides a nice counterpoint to the formula previously obtained by Hamahata, which is written in terms of several 1-dimensional parameters.

Keywords

drinfeld modules special functions and series expansions fractional calculus

Cite

@article{arxiv.1610.05976,
  title  = {A product formula for the higher rank Drinfeld discriminant function},
  author = {Dirk Basson},
  journal= {arXiv preprint arXiv:1610.05976},
  year   = {2023}
}

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10 pages

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