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arXiv · 2606.05771

Exotic and inverted Kloosterman sums over semisimple algebras

Daqing Wan·Dingxin Zhang
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Abstract

We introduce exotic Kloosterman sums and exotic inverted Kloosterman sums attached to non-commutative finite-dimensional semisimple algebras over a finite field $\mathbf{F}_q$, and prove their reduction formulae to exotic Kloosterman and exotic inverted Kloosterman sums over commutative \'etale $\mathbf{F}_q$ algebras. We then obtain square-root estimates for these sums; for inverted sums an explicit correction term may appear.

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Daqing Wan, Dingxin Zhang. 2026-06-04. Exotic and inverted Kloosterman sums over semisimple algebras. https://arxiv.org/abs/2606.05771

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