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arXiv · 1108.1292

On certain cusp forms on a definite quaternion algebra

Tommaso Giorgio Centeleghe
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Abstract

If $D$ is the definite quaternion algebra over $\qu$ of discriminant $p$, we compute, for any prime $p>3$, the number of infinite dimensional cusp forms on $D^*$ which are trivial at infinity, tamely ramified at $p$, and have given conductor $N$ away from $p$. We include a detail explanation of a Deuring--type correspondence between supersingular elliptic curves in characteristic $p$ and a certain double coset arising from the adelic points of $D^*$.

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Tommaso Giorgio Centeleghe. 2011-08-05. On certain cusp forms on a definite quaternion algebra. https://arxiv.org/abs/1108.1292

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