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arXiv · 2505.19654

Character sums over co-dimension one sub-lattices in finite field extensions

Aishik Chattopadhyay
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Abstract

We obtain nontrivial bounds for multiplicative character sums over codimension-one sublattices of finite field extensions $\mathbb{F}_{p^d}$. This extends earlier results of Davenport--Lewis and Chang from full-dimensional settings to the codimension-one setting. As an application, we establish cancellation in character sums over binary cubic forms for intervals of length $p^{3/8+\varepsilon}$. Our approach combines Burgess-type amplification technique, represesentation of character sum using multiplicative energy and it's estimates to prove the result.

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Aishik Chattopadhyay. 2025-05-26. Character sums over co-dimension one sub-lattices in finite field extensions. https://arxiv.org/abs/2505.19654

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