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September 29, 2025Open Access

A Short Character Sum in Fp³

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The analysis establishes bounds for character sums in finite fields, suggesting deeper structures in two-dimensional grids and higher lattices.

New bounds for short character sums are established, highlighting nontrivial cancellation in finite fields.
The sum exhibits cancellation uniformly in ω across intervals of size p^{3/8+ε}, showcasing significant results.
Generalization extends findings to codimension-one sublattices in higher dimensions, enriching existing results.
Alternative estimates for character sums on binary cubic forms provide further implications for number theory.

A. K. Chattopadhyay (2025) studied this question.

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The analysis establishes bounds for character sums in finite fields, suggesting deeper structures in two-dimensional grids and higher lattices.