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arXiv · 2512.11288

Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves

Tetsushi Ito·Daichi Takeuchi·Takahiro Tsushima
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Abstract

We study exponential sums on Witt vectors, known as Gauss--Heilbronn sums, and the curves whose Frobenius traces realize these sums via a Deligne--Lusztig type construction. For 3-typical Witt vectors of length two, we analyze Gauss--Heilbronn sums, from which we fully determine the Frobenius slopes of the associated curves.

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Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima. 2025-12-12. Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves. https://arxiv.org/abs/2512.11288

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